`int cot^5(theta) sin^4(theta) d theta` Evaluate the integral

`intcot^5(theta)sin^4(theta)dTheta=`

`int[(cos^5(theta))/(sin^5(theta))]sint^4(theta)dTheta=`

`int[(cos^5(theta))/(sin^(theta))]d(Theta)=`

`intcos^4(theta)[cos(theta)/sin(theta)]d(Theta)=`

`int(cos^2(theta))^2[cos(theta)/sin(theta)]d(Theta)=`

`int(1-sin^2(theta))^2[cos(theta)/sin(theta)]d(Theta)=`

Integrate using u-subsitution.

Let 

`u=sin(theta)`

`(du)/[d(theta)]=cos(theta)`

`d(theta)=(du)/[cos(theta)]`

`int(1-u^2)^2[cos(theta)/u][(du)/(cos(theta))]=`

`int[1-2u^2+u^4]/udu=`

`int[(1/u)-2u+u^3]du=`

`ln|u|-(2u^2)/2+u^4/4+C=`

`ln|u|-u^2+1/4u^4+C=`

`ln|sin(theta)|-sin^2(theta)+1/4sin^4(theta)+C`

The final answer is:  `ln|sin(theta)|-sin^2(theta)+1/4sin^4(theta)+C `