Integrating x(e^x): Step-by-Step Guide

  • Thread starter Thread starter theRukus
  • Start date Start date
  • Tags Tags
    Integral
theRukus
Messages
49
Reaction score
0

Homework Statement


What is the integral of x(e^x)?


The Attempt at a Solution


It's part of a larger question. I've got a midterm tomorrow and just realized I don't know the principles of integrating e^x other than that the integral of e^x is e^x. I've scoured my textbook and cannot find it. Could anyone provide insight?
 
Physics news on Phys.org
What you're looking for is integration by parts, which can be proven from the Product Rule. If

d(uv) = v du + u dv

Then subtract v du and integrate:

\int u dv = \int d(uv) - \int v du = uv - \int v du
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
Replies
7
Views
2K
Integration problem using inscribed rectangles
Replies
14
Views
2K
Integral of e^cosx: Answers Sought
Replies
11
Views
2K
Complex contour integral proof
Replies
1
Views
996
Integral of a Recursive Function
Replies
3
Views
2K
How do I change this integral limit from x to t?
Replies
2
Views
2K
The indefinite integral and its "argument"
Replies
3
Views
2K
How Do You Correctly Apply Integration by Parts to ∫-e^(2x)*sin(e^x) dx?
Replies
9
Views
2K
Fourier transform of integral e^-a|x|
Replies
6
Views
3K
Finding the Fourier cosine series for ##f(x)=x^2##
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top