Evaluate integral of (e^6x)/sqrt(1-e^2x)dx
p.s: Will U be equal to e^x?

Question

Evaluate integral of (e^6x)/sqrt(1-e^2x)dx
p.s: Will U be equal to e^x?

anonymous · Answer

Is arcsin(u) x (u^6/6) correct?

sirm3d · Answer

nope. you can use integration by parts or trigonometric substitution.

sirm3d · Answer

a simple substitution will also work,
$$y=1-u^2\dy=-2udu\u^5du=u^2u^2(udu)$$

anonymous · Answer

i used trigonometric subs. 
e^x as u. then it end up at
integral of (u^5)/sqrt(1-u^2) du !!!

anonymous · Answer

1/sqrt(1-u^2)du is arcsin (u) 
and the top is u^5 du so u^6/6 
so wouldnt everything b equal to arcsin(u)x(u^6/6) ???????

sirm3d · Answer

you can even use the substitution $$w=\sqrt{1-u^2}\w^2=1-u^2\2wdw=-2udu$$

sirm3d · Answer

the integral of a product f(x) g(x) follows the integration by parts method, especially if other methods won't work.

anonymous · Answer

y do i get everythin wrong. i thought i did this one right at least-.-; haha

anonymous · Answer

i think ur using some other method that i havnt learned...
im only familiar with the u-sub method. and idk how you bring in y or w ! : (

sirm3d · Answer

u-sub is the same as w-sub, or y-sub. you are free to choose a variable other than u.