How Do You Integrate (cos(x))^2(tan(x))^3?

[Rasine]

find the integral of (cosx)^2(tanx)^3

so first of all i rewrote tan to be (sinx)^3/(cosx)^3 so that i could cancle out the (cosx)^2 on top

and now i have the integral of (1/cosx)(sinx)^3

i rewrote that to be (tanx)(sinx)^2...and now i am stuck

i don't know of any IDs that could make the integral simplier...i am open to suggestions

 

[neutrino]

\frac{\sin^3{x}}{\cos{x}} = \frac{\sin^2{x}sin{x}}{\cos{x}}

 

[Rasine]

right...so sinx/cosx would be tanx and that would it it (sinx)^2(tanx)...right?

 

[neutrino]

No. sin^2 would be 1-cos^2

 

[Rasine]

ok let me try that

 

[Rasine]

now i am getting the integral of tanx-sinxcosx

i know how to integrate sinxcosx but not tanx

 

[neutrino]

i know how to integrate sinxcosx but not tanx

That's strange...

tanx is just sinxcosx, except that the cosx is placed in the denominator.

 

[Rasine]

oohhh ok...let me try it