# Thread: trig sub. intregration problem

1. ## trig sub. intregration problem

i'm currently trying to integrate....
e^(x)*sqrt(1-e^2x)

i used x = sin(theta)....

i'm just unsure what to do about the left side of the equation,i understand cos(theta) takes the place of...sqrt(1-e^2x)..but how/what takes the place of e^(x) is it just sin(theta)? -thx

e^(x)*sqrt(1-e^2x)

2. To remove that front e^x let $u = e^x \implies du = e^x dx$ which gives $\displaystyle \int e^x \sqrt{1-e^{2x}}\, dx = \int \sqrt{1-u^2}\, du$ (I have subbed in $du$ for $e^x dx$)

Then carry on with your trig sub

3. Originally Posted by maybnxtseasn
i'm currently trying to integrate....
e^(x)*sqrt(1-e^2x)

i used x = sin(theta)....

i'm just unsure what to do about the left side of the equation,i understand cos(theta) takes the place of...sqrt(1-e^2x)..but how/what takes the place of e^(x) is it just sin(theta)? -thx

e^(x)*sqrt(1-e^2x)
Use the substitution

$e^{x}=\sin(t) \implies e^{x}dx=\cos(t)dt$

Putting this into the integral gives

$\displaystyle \int e^{x}\sqrt{1-(e^{x})^2}dx=\int \sqrt{1-\sin^2(t)}\cos(t)dt=\int \cos^2(t)dt$