What is the Integral of sin x * sqrt(1+cos2x)?

[wlooi]

Homework Statement

∫(sin x)√(1+cos²x) dx

 

[HallsofIvy]

What you have written makes no sense (even if the latex were working). you have \sqrt{} with nothing inside the square root and have a subscript that makes no sense.

Did you mean $\int sin(x)\sqrt{1+ cos^2(x)}dx$?

If so, start by letting y= cos(x).

 

[wlooi]

Yes, that's exactly what I was try to make. Well, this is my first time using this so sorry..

 

[wlooi]

Well, I got myself until:

$\large -$ $\int \sqrt{1+y^2}$ $\large dy$

then I stucked again.

 

[Dick]

Well, I got myself until:

$\large -$ $\int \sqrt{1+y^2}$ $\large dy$

then I stucked again.

Try and think of a trig (or hyperbolic trig) substitution that will turn 1+y^2 into the square of something so you can get rid of the square root.

 

[wlooi]

Argh... I don't seem to get it after cracking my head for a while. Can I have a little bit more tips?

 

[SammyS]

Let's see, ...

1+tan²(θ) = sec²(θ)

1+sinh²(u) = cosh²(u)

 

[wlooi]

using 1+tan²v=sec²v , I got it until :

-∫sec³v dv

am I suppose to do by parts or is there other ways?

 

[Dick]

using 1+tan²v=sec²v , I got it until :

-∫sec³v dv

am I suppose to do by parts or is there other ways?

Parts. Split it into sec(v)^2*dv and sec(v).

 

[wlooi]

Okay, I think I got it. Thanks for the help from everyone.^^