sin3 x cos2 x dxSolutionlet sinx t cosxdxdt so integral beco

Solution

let sinx= t
=>-cosxdx=dt
so integral becomes
t^3(1-t^2)dt

now let t^2=m

=>2tdt=dm

=so integral becomes

=>0.5(m(1-m))dm

=now applyin integration by parts

0.5(m[(1-m)dm] -[(1-m)dm])

=0.5(-m*(-2)/(1-m)- 2/(1-m)]

=>(m/(1-m)-1/(1-m))

=>-((1-m)

=-((1-t^2)

=-(1-sin^2x)

=-cosx+c