Cos^3(x)sin2(x)dx?

Question

Cos^3(x)sin2(x)dx?

Answer 1

∫cos^3Xsin2Xdx

firstly put

sin2X=2sinXcosX

now

=∫cos^3X(2sinXcosX)dX

=∫2cos^4XsinXdX

now

take cosX=t

differentiating it

-sinXdX=dt

sinXdX=-dt

now putting it in equation

-2∫t^4dt

(-2t^5)/5+c

c= constant

put t=cosX

(-2cos^5X)/5+c

answer is

∫cos^3Xsin2XdX

=(-2cos^5X)/5+c

where c is constant