# 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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### Why does Mathematica choose branches as it does in this situation?

Consider these integrals: ...
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### integrate giving wrong result

Bug introduced in 7.0 or earlier and persisting through 10.4.1 or later A question with the same title has been asked many times, but I can't find the solution of my problem in their answers. The ...
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### Strange behaviour of integrals with Cos, Sin, and Exp

During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would consider it a bug. ...
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### Is there a way to teach integrate new solutions?

I have an integral which I can solve, but integrate cannot: ...
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### Strange kernel segmentation fault in Integrate

Bug introduced in 8.0 or earlier and persisting through 10.4 Define tointegrate = D[V[y1[t], y2[t]], y2[t]] D[V[y1[t], y2[t]], {y1[t], 2}] and try to find its ...
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In harmonic analysis, pseudodifferential operators are a way to generalize the notions of derivatives, through the use of Fourier transforms. The basic idea being, Let $u(x)\in\mathcal{S}(\mathbb{R}^... 0answers 145 views ### Function for the Second Derivative Test I wrote the following function. It is based on Mathematica for Rogawski's Calculus, 2nd Ed, 2007, Based on Mathematica 7. See: http://users.rowan.edu/~hassen/Math_Rogawski_Calc.htm, Chapter 14. I made ... 0answers 54 views ### Indeterminate expression 0(I*Infinity]) on indefinite integrals on first use only I do not know if this is new or not, I googled before. Windows 7, 10.1 64 bit: Integrals generate this error message The strange thing also is that the message shows up the first time the command ... 0answers 578 views ### Symbolic matrix calculus: What's new in Version 9 I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ... 0answers 106 views ### Derivative of generating function (Example from documentation) In the documentation for GeneratingFunction, the following example is given under Examples -> Properties & Relations -> Derivative: ... 0answers 62 views ### Why do I need to generalize/parameterize an integral sometimes to get a closed form result? ... 0answers 231 views ### Is this result wrong because of calculation time? (and more questions about Assumptions) I am confused with the Integrate Given by Mathematica. First let's see a one-dimensional case: ... 0answers 247 views ### Numerical-Symbolical Integration (Calculus) I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ... 0answers 109 views ### Bug in the “PrincipalValue” method of NIntegrate? Update 2 The technical support suggests setting AccuracyGoal. As I quote here It does appear that the program is returning an incorrect result along with a ... 0answers 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, ... 0answers 65 views ### Cauchy Principal Value Cauchy principal value of the following integration gives nothing in Mathematica.$\int\limits_{-\infty}^\infty\frac{\text{dx}}{x-2}$I tried some hand calculation which is$\lim\limits_{\...
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I got a question concerning an integral. I need to know the analytical expression. I have to Mellin transforn a function and the integral is then sth. like this:  \int x^{N-1} \frac{Ln(a -x)}{1-x} ...
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### Good coding for integral substituions

This question is aimed at improving both my coding and my understanding of MMa's capabilities. A lot of my code is still hacks and workarounds for things I don't know how to do properly. I want to ...
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### Derivative of vector dot product with respect to a vector

I have the expression: Transpose[gvecI, {2, 1}].x (m[1] + m[2]) gvecI and x are [3x1] ...
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### Converting integral equations to differential equations

I am trying to use Mathematica to convert integrals to differential equations, of any order. An example of an integral equation is given below, in Mathematica code. Could you please advise as to the ...
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### Computing an inexact derivative with some terms preserved in exact form

I am beginning to learn Mathematica and have the following question: How can I return a derivative with exact numbers instead of one involving numerical approximations? My original, single variable ...
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### Evaluating an integral

Here is the input: Integrate[E^(2 I*t)/(2*Pi*(E^(I*t) - z)), {t, 0, 2 Pi}] and here the output: ...
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### Result of symbolic integration changed drastically by making assumptions

I would like to know the underlying reason for different outcomes for the two integration operation below. One of them includes a few assumptions, otherwise both have the same integrand: ...
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### Result of Integrate depends on order of integration although the domain is rectangular

The following: ...