1
vote
3answers
60 views

indefinite integral computation $dx/(e^{-x}-x)$

Hi i'm trying to carry out the following indefinite integral: $$\int \frac{1}{e^{-q} - q} \, dq$$ mathematica is not helping me, and i think it is not solvable by substitution method. any idea on ...
0
votes
0answers
56 views

Mathematica Integrate gives back the integrand

i'm trying to Integrate the following function: (q (1 + q) - E^-q Sinh[q])/(-q + Cosh[q] Sinh[q]) - ( 2 q Tanh[q])/(-q + Cosh[q] Sinh[q]) I already solved ...
0
votes
2answers
57 views

Difficulty finding Expectation of a special function

I have a special function given as: $${\rm f}\left(r\right) ={1 \over \beta\lambda}\,2^{r/\beta} \exp\left({\left[2^{r/\beta} - 1\right]K \over \lambda}\right)$$ I should find the Expectation of ...
3
votes
1answer
66 views

Why these integrals are evaluated differently? $\cos(x)/(a-b\cos(x))$

In attempt to solve electrostatics problem I came up to this integral that I am trying to integrate: $$\int_0^{2\pi}\frac{\cos(x)}{a-b\cos(x)} \, dx$$ where $a>b$ and both are real numbers. For ...
4
votes
0answers
115 views

How to integrate $\left(1+\ln(x)\right)\sqrt{1+(x\ln(x))^2}$ with Risch algorithm?

How would you integrate $\left(1 + \ln\left(x\right)\right)\, \sqrt{1 + \left(x\ln\left(x\right)\right)^{2}\,}$ using the Risch algorithm? I want to know this because Mathematica is using the Risch ...
1
vote
2answers
89 views

Bessel function to $\sin(kr)$

$J_{\frac{1}{2}}(kr)=\frac{\sqrt{\frac{2}{\pi }} \text{Sin}[\text{kr}]}{\sqrt{\text{kr}}})$ This can be easily obtained by Mathematica, How to do the details?
0
votes
1answer
140 views

Inverse Fourier transform to find out $\hat c_1$

If we have an integration which is need to solve inversely $$a_0 e^{-r^2/R^2} = \int_0^\infty \hat{c}_1(k) \frac{\sin(k r)}{r} dk,$$ If I transform the $\sin(kr)$, then we get imaginary part. Please ...
1
vote
0answers
302 views

$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$

I'm trying to solve the integral $\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$, where $s$, $r$ and $m$>1 are positive integers. My question is whether a closed form ...
1
vote
2answers
122 views

Unexpected results when integrating definite integral with variable bounds

When I plug something like this into Mathematica: $$\int_0^{x^2-1} k y \, dy$$ I get exactly what I would expect: $$\frac{k}2 (x^2-1)^2 $$ However, when I change my bounds ever so slightly, from ...
0
votes
2answers
163 views

Integrating with vector coefficients in Maple

I'm trying to use Maple to do something like this integral: $\displaystyle\int \frac{a\mu-b}{||a\mu-b||^3} \mathrm{d}\mu$ Where $a, b$ are vectors and $\mu$ is a scalar I'm integrating by. But I ...
1
vote
1answer
62 views

can't figure out what I been doing wrong on simple integration question

$$\int_0^1 \sqrt{(\sqrt{5})^2+(2t)^2}\;dt$$ Based on the formula $\int \sqrt{a^2+x^2}\;dx=\frac{1}{2}[x\sqrt{a^2+x^2}+a^2\log(x+\sqrt{a^2+x^2})]$ I just plug in above input into the formula above ...
2
votes
1answer
227 views

Two questions on integration of $\operatorname{sech}x$, one with Mathematica

So I have a two fold question, one I believe is simple but my algebra seems to be off, the other involves the trapezoidal rule of integration using Mathematica as an aid. Here they are: $1.\quad ...
0
votes
1answer
206 views

Automated generation of a parametric plot?

Currently we are introducing integrals of manifolds in $3d$-Space in a course. We are given some set $E \subset \mathbb{R}^3$ and should evaluate the surface and scetch how it looks. For example ...
-3
votes
1answer
245 views

How to solve this integral of trigonometric f in Mathematica

How to solve this integral in Mathematica Is it possible to solve it numerically? $$\begin{align} \int_{-1}^1 \cos\big(&(.75-.75x^2)\cdot y_1 + (.25 - .5x - .75x^2) \cdot y_2 \\ + &(-.5x ...
2
votes
1answer
536 views

Fourier transform in Mathematica

When I calculate the Fourier transform of the function $$f(t) = \mathrm e^{-|t|/\tau} \text{ with } \tau >0$$ in Mathematica once via the function FourierTransform and once by hand, I get different ...
1
vote
2answers
153 views

Taking advantage of linearity of integration in Mathematica

I want to evaluate an integral of form given below $$\int\limits_\alpha^\beta (f(x) + g(x) + h(x) + ...) dx$$ When I give it to Mathematica it takes forever to evaluate. But if I give it in this ...
0
votes
1answer
183 views

Equation to find if a set of vertices form a concave shape?

i'm trying to get around the rule of only being able to form concave shapes in the SFML c++ library by forming the non-concave shape out of many concave shapes. What I don't know is the equation for ...
4
votes
2answers
500 views

Integrate in Mathematica takes forever

I'm trying to calculate the length of a curve from a polynomial in Mathematica and for some reason Integrate doesn't complete, it just runs until I abort the execution. The polynom: ...
3
votes
2answers
857 views

Compute unknown limit from known integral in Mathematica?

I have an integral $\int_a^b \! f(x) \, \mathrm{d}x = c$ where I know c and either a or b. Now I want to compute either b or a (i.e., the missing limit). How would I do that in Mathematica/Wolfram ...