fulli stumped no.2 (1 Viewer)

[joeylike2hiphop]

omg i knew de question i typed last time was 2 freaken easy. anywais de question was actualli
&int 1/(sqreroot(1+sin2x))dx
i got up to the step where it is down to
&int 1/(sinx+cosx) dx
i think u use t formula for this but then it gets really complicated. i dun noe the answer for this question so please help u guys. fanks heaps

 

[joeylike2hiphop]

blah

sorri question is
∫ 1/ (sqreroot(1+sin2x)) dx
and den it becomes
∫ 1/(cosx+sinx) dx
den try t formula i dunno not sure but im stumped, fanz ppl

 

[Jumbo Cactuar]

use t substitution;

let t = tan(x/2)

dx = 2dt / (1+t²)
sinx = 2t/1+t²
cosx = 1-t²/1+t²

∫ dx/(cosx +sinx) = 2 ∫ dt/(-(t²-2t+1) +2)
=2 ∫ dt/(2-(t-1)²)
=ln(|2^1/2+(t-1)/2^1/2-(t-1)|)/2^1/2 + C
=ln(|(2^1/2-1+tan(x/2))/(2^1/2+1- tan(x/2))|)/2^1/2 + C , x /= 3pi/4