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5 votes

Reduce or Limit to have positive value!

The result of the command Reduce[Tanh[x]/Sqrt[-1 + Tanh[x]^2] > 0, x, Reals] False says there is no real solution. The ...
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5 votes
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Plotting, Integrating two variable function with cross-restricted domain

For the plot you can use RegionFunction, which takes a pure function which takes x, y, and z values:: ...
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9 votes

Integral of orthogonal Bessel functions

The OP's integral is missing information about the subscripted variables (which I avoid) and the change of coordinates leading to the interval from b to ...
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0 votes

Solving elliptic integrals in Mathematica

The machinery I presented in this answer can be used to obtain a result in terms of the Carlson symmetric integrals. To wit, ...
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2 votes

Plot for DSolve in mathematica

...
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3 votes
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Integration over an implicit region

You want the region of integration to be defined by inequalities, rather than equalities. Your region can be described as follows: ...
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3 votes

Symbolic scalar-by-matrix derivative

I tried the NCAlgebra package: << NC`; << NCAlgebra`; SNC[X, A] NCGrad[tr[tp[tp[X] ** A] ** (tp[X] ** A)], A] And ...
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2 votes

Mathematica 13.0 simplifies trigonometric integral wrong

Under natural assumptions one obtains ...
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8 votes

Mathematica 13.0 simplifies trigonometric integral wrong

Here's a way to eliminate the singularities in the answer, provided you can be happy removing a singularity of the form Sin[u]/u with ...
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11 votes
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Mathematica 13.0 simplifies trigonometric integral wrong

It's not too uncommon for Integrate to return something which has a special case that can't be evaluated properly without taking a limit. In your case there is a ...
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2 votes

Getting the same result from Integrate as Probability

Got it figured out, Mathematica just wants some assumptions about the integration variables and needs GenerateConditions->False: ...
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1 vote

Numerical Plot for an example

When we use NDSolveValue, the result sol is the interpolation function. It is difference to ...
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1 vote
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Integrate: slow and wrong results

To investigate what's happening during the integration try using EvaluatioMonitor or StepMonitor.
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1 vote

Integrate: slow and wrong results

In version 13 on Windows 10 ...
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1 vote

Incorrect result of AsymptoticSum

Remove the assumptions concerning a > 0 && a < 1 ...
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7 votes

Can Mathematica calculate this elliptic, triple integral?

If you regard symmetry of integrand (two times integral from 0<b<a) and rearange to do integration over c at last, you get the result in a non splitted integration in 10 seconds. Original ...
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10 votes

Can Mathematica calculate this elliptic, triple integral?

The unevaluated integral that Mathematica produced in the OP can be massaged a bit. First, note that due to symmetry, we can instead consider the integral ...
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1 vote

Taking sentences with a spatial factor

The TeX you posted is weird for a few reasons there's $t()$ and $z()$ there's $z$ multiplied by $\text{z}$; I'm taking these to be different variables Regardless, it was quick to write in ...
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0 votes

Incorrect result of AsymptoticSum

There is a workaround: ...
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23 votes
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Can Mathematica calculate this elliptic, triple integral?

Doing the Integrals separately for a, b and c gives the answer $\frac{128}{45 \pi}\sim 0.905415$, which agrees with the numerical estimate from NIntegrate: ...
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5 votes
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How come I can't get $\int f(t)$ from performing derivative/anti-derivative operation on $\int f(t)$?

Does this do the trick? ...
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5 votes
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How to integrate this product of Exp[] and Cos[] using Mathematica

Besides of the method provide by @Michael E2,we can test the result by N-L formula. ...
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5 votes
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Selecting a solution range that is independent of a variable value

Resolve [ForAll[x, D[x^3 - 3 a x^2 + 3 a x - 2, x] >= 0]] 0 <= a <= 1
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7 votes
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Evaluating PlusMinus to 2 decimal answers

Clear["Global`*"] a = Around[1, 1] a == Around[NormalDistribution[1, 1]] (* True *) b = Around[3, 1] ...
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0 votes

The inverse Laplace transform alters parameter constraints

Too long for a comment. You apply the result of ...
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0 votes
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`Assuming` combined with mathematical notation of `Integrate`

I found the issue. The solution was in the examples section of Integrate. The syntax error is with the superscript ^ after ...
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0 votes

`Assuming` combined with mathematical notation of `Integrate`

There is a syntax error with Subscript Try ...
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3 votes

How to perform the first and second derivatives of Nth polynomials?

You should have shown your own attempts. Anyway, try this s = Sum[a[i, j]*x^i*y^j, {i, 0, n}, {j, 0, n}] Then D[s, x] yields <...
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4 votes
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Inconsistent results between NIntegrate and Integrate

If you look at the result of ...
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1 vote

Limit is not actually evaluated, but wolframalpha does

f[x_] := 1/(1 + a^2/(4 x (a - x)) Sin[b Sqrt[a - x]]^2) Limit[f[x], x -> a] $$\frac{4}{a b^2+4}$$
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1 vote

Limit is not actually evaluated, but wolframalpha does

Correcting your syntax and assuming a and b real, one obtains ...
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4 votes

How do we just have $\log$ solution?

This is a separable ODE of the first order. Let us make one step by hand and obtain ...
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3 votes

The jumping problem when rolling reuleaux triangle

Daniel Huber's code seems to let the points and edges slide a little. In order to ensure no slippage, you need to use the perimeter of the shape: each arc has length $\pi/3$, so the distance between ...
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2 votes

The jumping problem when rolling reuleaux triangle

With code from the Wolfram Demo project for a Reuleaux triangle from https://demonstrations.wolfram.com/ARotatingReuleauxTriangle/ and some small changes: ...
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7 votes

Poincare section for a perturbed string

Small modification leads to appearance of random behaver and solves step size problem ...
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4 votes
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How to get the derivative from this implicit equation with differentials?

expr = y^3 Dt[x] + 3 x y^2 Dt[y] + Cos[x + y] (Dt[x] + Dt[y]) (Dt[y] /. First@Solve[expr == 0, Dt[y]])/Dt[x] // Simplify -((y^3 + Cos[x + y])/(3 x y^2 + Cos[x + ...
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2 votes

How to set integral starting from 0 in the symbolic solution to ODE

I used a dummy variable in DSolve returning "Indeterminate" to set location of the initial condition, which in turn sets the starting point for an unevaluated integral. But in this case we ...
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2 votes

How to set integral starting from 0 in the symbolic solution to ODE

I would like the solution to integrate from 0, instead of 1 ...
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3 votes

Plot the general and a particular solution for this differential equation

Manipulate parameters to get overview ...
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3 votes

Plot the general and a particular solution for this differential equation

Draw the slope field for the general solution. There are two solutions. Pick one ClearAll[y,x]; ode = y[x]^2*y'[x]^2 == 1 - y[x]^2; sol = Solve[ode, y'[x]] Lets ...
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4 votes
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How Implicit differentiate in order to get a differential equation

The first equation is: eqn1 = (x - a)^2 + y^2 == 1; ReplaceAll y to create a function ...
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4 votes

How to test a recursive formula using Mathematica?

For a fully recursive implementation, for which @kenric gives an outline, the definition must be inductive. In particular, you need a base case (or more in some cases, like for the Fibonacci recursion)...
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