$\displaystyle \int 33\frac{cos^5(x)}{\sqrt{sin(x)}}$
Should I begin by splitting up the numerator? Multiplying by the conjugate? I've tried those two and some others to no avail.
THanks
Put
$\displaystyle
sin(x) = t
$
$\displaystyle cos(x)dx = dt$
$\displaystyle 33\int \frac{cos^5(x)dx}{\sqrt{sin(x)}} $
$\displaystyle = 33\int \frac{cos^4(x)dt}{\sqrt{t}} $
Now
$\displaystyle cos^4(x)$
$\displaystyle = (1 -sin^2(x))^2$
$\displaystyle = (1 - t^2)^2 $
$\displaystyle = 1 + t^4 - 2t^2 $
Hence integration becomes
$\displaystyle = 33\int \frac{(1 + t^4 - 2t^2 )dt}{\sqrt{t}} $
Now go ahead and ask incase of trouble
By last question, do you mean this post?
http://www.mathhelpforum.com/math-he...ig-powers.html
$\displaystyle 33\int sin^{-1/2}(x)cos^4(x)cos(x)dx$
$\displaystyle 33\int sin^{-1/2}(x)[1-sin^2(x)]^2cos(x)dx$
$\displaystyle u = sin(x)$
$\displaystyle du = cos(x)$
$\displaystyle 33\int u^{-1/2}(1-u^2)^2du$
Is this the right way?
Edit: It's the right way, thanks for the help