# Tagged Questions

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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### Symbolic Integrate fails after almost 1 hr calculation

Mathematica 9. I want this Integrate[( Cos[t ω]^2 Cos[α + t ω])/(-1 + A Cos[α + t ω])^2, {t, 0, (2 π)/ω}] Can Mathematica handle with it? I tied different ...
135 views

### Residue failed to reproduce this residue in a paper

This problem is a more clearly state of my original problem which is off topic, so I reconsider my problem carefully based on previous discussions, and gives the following valid code to reproduce my ...
59 views

### Integral of $(\sin x)^3(\cos x)^3$ [closed]

For the integral of (sin x)^3(cos x)^3 I got 1/6(cos x)^6 - 1/4(cos x)^4 + C. This seemed to work but my book had 1/4(sin x)^4 - 1/6(sin x)^6 + C. This is similar to what I got but instead of cosine ...
62 views

### Why does Expectation function compute, while explicit integration does not?

The code: Expectation[1 + 1/y, {y \[Distributed] ExponentialDistribution[1]}] outputs 1 - EulerGamma While, ...
130 views

### NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
66 views

### Problem in limit of exponential function

I want to obtain Exp[-α/(1 - α)] /. {α -> 1} The output is Indeterminate. But I calculate without Mathematica and I ...
64 views

### Need help on simplifying the integral of a square root of a polynomial

I have the following expression a = 4 Cos[af / 2]^2; b = 1 - 5 Cos[af / 2]^2; c = Cos[af / 2]^2; s = Sqrt[a*x^4 + b*x^2 + c] and I need the integration of $s$ in ...
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### Symbolic and numeric limit disagreeing on branch cut of ArcTan

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. Investigating comments to my previous question lead me to the following problem: ...
158 views

### Integrate and NIntegrate disagreeing over branch cut of Sqrt?

Bug introduced after v8.0.4 and before v9.0.1, and persisting through v10.4.1. In Mathematica 10.2 I'm trying to integrate this piecewise continuous function, but ...
52 views

### nonatomic expression expected when trying to sum of the integrals of two functions

newbie to MMA. After computing the following two integrals: ...
54 views

### Issue while trying to compute the integral for the coefficients of a triangular wave

I was trying to compute these integrals in order to check if I was correct: or in code ...
59 views

### What does Mod^(1,0) mean in mathematica output [closed]

I am trying to take he derivative of mod(remainder). In:= D[Mod[x, y], x] Out = Mod^(1,0)[x,y] I cannot understand the meaning of Mod^(1,0). What does the ...
103 views

### Integral over real valued function becomes complex

I've tried to solve the following integral, but I get a complex solution even tough it should only have a real part. $$f(x)=- \frac{10^{-20} x}{0.99005- e^{10^{-12}x}}$$ Now I want to calculate the ...
68 views

### How to integrate with integer parameter in Mathematica?

I would like to integrate the following expression with N being Integer ...
165 views

### Wrong limit: Limit[(1 + (-1)^n/n)^n, n -> Infinity]=1 (Mathematica 10.4 and W-Alpha)

Since $(1-\frac{1}{n})^n\to 1/e$ and $(1+1/n)^n\to e$, the sequence $(1+\frac{(-1)^n}{n})^n$ has no limit as $n\to\infty$, but has limits for odds and even numbers. If $n$ were taken to be real, there ...
251 views

### Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions

Bug introduced in 7.0 or earlier and persisting through 10.4.1 This is a follow-up to this question regarding numerical instabilities occurring with modified Bessel functions. In trying to explore J....
74 views