# Questions tagged [calculus-and-analysis]

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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434 views

### Strange behaviour of integrals with Cos, Sin, and Exp

Bug introduced in 8.0.4 or earlier and persisting through 13.0.0 During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would ...
326 views

### Is there a way to teach integrate new solutions?

I have an integral which I can solve, but integrate cannot: ...
277 views

### Series with ArcTan gives wrong symbolic answer in Wolfram Language

Bug introduced after 9 and persisting through 13.1 Recently, I have found a very bad problem with Wolfram Language. It gives the wrong answer for a quite simple expression! When calculating ...
142 views

### Reduce: Var is not a valid variable

Bug introduced in 12.3 or earlier and persisting through 13.1 or later I am trying to integrate the following but it returns a Reduce::ivar warning message. ...
314 views

### Possible Symbolic Integration Bug

Bug introduced between 5 and 8 and persisting through 12.0. I think I may have found a bug, and want to verify is this reproducible in other versions and platforms and not a mistake of mine. I ...
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209 views

### Mathematica gives wrong answer for a definite integral

I tried to compute the definite integral Integrate[Exp[Pi I t]/((-I + 1 + t) Cosh[Pi t]), {t, -Infinity, Infinity}] and obtained the answer (version 11.2.0.0) ...
160 views

### Convoluting inverse square root with Gaussian

Bug introduced in 9.0 and persisting through 11.0.1 or later I would like to convolute the inverse square root on the interval [0,inf] with a Gaussian function, ...
254 views

### Strange Integrate behavior (a bug!)

The following two calculations should give the same result. After all, integration is a linear operation. I have pasted the code below in case you want to play with it. ...
125 views

### Numerical verification of the estimate:

How to verify numerically with considerable accuracy in Mathematica the following : $$\int_2^x\dfrac{1}{z\Gamma(\sin^2[π\Gamma(z)/(2z)])}dz\sim\ln(\ln(x))$$ ? I need more suitable and better code ...
202 views

### Incorrect result by DSolve

For real $x$ consider the trivial equation $$|y'(x)|=-|x|.$$ Since the left side is always positive and the right always negative, there is no solution. Let's try ...
250 views

### Help implementing Magnus Expansion

The Magnus expansion is a tool to approximate solutions to first-order linear differential equations (the Wikipedia page is quite instructive and concise) - it's particularly useful because all orders ...
182 views

### Integrating a product of three Spherical Harmonics

The following command is returned unevaluated. The answer is well known to be related to Wigner's 3j Symbol which is also a defined function in Mathematica. ...
517 views

130 views

### Integration involving DiracDelta

I tried the following integration Integrate[DiracDelta[Tan[x]], {x, -4, 4}] I got 1 as the result. However, between -4 and 4 ...