How do I do this trig. integral?

[shreddinglicks]

Homework Statement

∫cos(x)^5 / sqrt(sin(x))dx

Homework Equations

∫cos(x)^5 / sqrt(sin(x))dx

The Attempt at a Solution

i tried to break up cos(x)^5

∫(cos(x)^2)(cos(x)^3)dx

I tried an identity

(1-sin(x)^2)(sin(x)^-.5)cosx^3

I tried to distribute the sin(x)^.5 and use a u sub but that's where I get stuck.

 

[STEMucator]

Write the integral as:

$\int \frac{cos^4(x)cos(x)}{\sqrt{sin(x)}} dx$
$= \int \frac{(1-sin^2(x))^2cos(x)}{\sqrt{sin(x)}} dx$

$u = sin(x).. du = ..$

 

[shreddinglicks]

Write the integral as:

$\int \frac{cos^4(x)cos(x)}{\sqrt{sin(x)}} dx$
$= \int \frac{(1-sin^2(x))^2cos(x)}{\sqrt{sin(x)}} dx$

$u = sin(x).. du = ..$

I see, and du = cos(x)

that takes care of my cos(x) in the numerator but it doesn't take care of the identity.

 

[STEMucator]

I see, and du = cos(x)

that takes care of my cos(x) in the numerator but it doesn't take care of the identity.

Of course it does. If $u = sin(x)$ then $u^2 = sin^2(x)$.