`int sin^3(theta) cos^4(theta) d theta` Evaluate the integral

`intsin^3(theta)cos^4(theta)d theta`

Rewrite the integrand as,

`=intsin^2(theta)sin(theta)cos^4(theta)d theta`

Now use the identity: `sin^2(x)=1-cos^2(x)`

`=int(1-cos^2(theta))sin(theta)cos^4(theta)d theta`

Now apply integral substitution.

Let `u=cos(theta)`

`=>du=-sin(theta)d theta`

`=int-(1-u^2)u^4du`

`=-int(1-u^2)u^4du`

`=-int(u^4-u^6)du`

`=-intu^4du+intu^6du`

`=-u^5/5+u^7/7`

Substitute back `u=cos(theta)`

`=-1/5cos^5(theta)+1/7cos^7(theta)`

Add a constant C to the solution,

`=-1/5cos^5(theta)+1/7cos^7(theta)+C`