<p>Here is an integration problem involving trig substitutions...</p>
<p>integrate (e^x * ((1-(e^2x))^1/2)dx</p>
<p>so, I let e^x = sin (theta)...I got the problem done until the part where you convert theta's at the end back in terms of x.</p>
<p>somebody solve it, i did it and then got lost in my substitution variables. somebody help. lol</p>
<p>haha...I think you got stuck where I did</p>
<p>Why use sin(theta)=e^x. Use U Substition. What book did the problem come from.
I can work it out when I get home if yall want.</p>
<p>I got 1/2[arcsin(e^x)+ (e^x)((1-e^2x)^1/2)]
is that the answer?</p>
<p>yeah, that's the answer...I ended up getting it. I was stuck at what to do with the sin 2theta (after integration, while trying to convert back to algebraic form)....and you can use the property 2<em>sintheta</em>costheta</p>
<p>nice job seahorse. i got it today at school during english class........lol. i got e^x = sintheta, but then was having trouble getting the relationship between dx and dtheta, but then i finally say theta = arcsin (e^x) and then realized i would have to do stuff with the sin inverse and solve the problem. cool integral if you ask me.</p>