Register to reply

How do I Integrate this! u substitution with limits.

Share this thread:
Feb21-12, 04:15 AM
P: 134
1. The problem statement, all variables and given/known data

Find ∫e^x/ (1+e^2x). dx , with limits ln 2 & 0
given u= e^x

2. Relevant equations

3. The attempt at a solution

u= e^x
du/dx = e^x
dx= du/e^x

sub limits of ln2 & 0 → u

Hence, limits 2 & 1


∫u* (1+e^2x)^-1* du/e^x

= ∫ u/ (u + e^3x)
= ∫ u/ e^3x
= ∫ 1/e^2x

= -e^-x
= -1/u
plugging in limits of 2 &1

Therefore, 0.2325...

Although i could not find this on the answer sheet did i do something wrong?
Please help, Thankyou.
Phys.Org News Partner Science news on
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
Feb21-12, 06:06 AM
P: 38
Should it become this?
= [itex]\left[\frac{ln(1+u^{2})}{2u}\right]^{2}_{1}[/itex]
Feb21-12, 06:16 AM
Sci Advisor
PF Gold
P: 39,556
Quote Quote by th4450 View Post
Should it become this?
Yes, this is correct. Letting [itex]u= e^x[/itex], [itex]du= e^xdx[/itex] so the numerator is just du and [itex](1+ e^{2x}[/itex] becomes [itex]1+ u^2[/itex]

= [itex]\left[\frac{ln(1+u^{2})}{2u}\right]^{2}_{1}[/itex]
However, this is incorrect. Yes, [itex]\int 1/u du= ln|u|+ C[/itex] but if you have a f(u) rather than u, you cannot just divide by f'(u)- that has to be already in the integral in order to make that substitution.

Instead, look up the derivative of arctan(u).

Feb21-12, 09:06 AM
P: 38
How do I Integrate this! u substitution with limits.

Oops haha
should let u = tanθ

Register to reply

Related Discussions
Do I integrate it using Trigonometry substitution? Calculus 4
Integrate by substitution Calculus & Beyond Homework 3
Integrate exp(-(x^2)) using the substitution u=tanh(x) Calculus 8
Integrate using trig substitution Calculus & Beyond Homework 6
How to integrate without trigonometric substitution Calculus 2