Evaluate the following. ∫cos5(3z)dzsin2(3z)

Lennie Carroll

Lennie Carroll

Answered question


Evaluate the following.

Answer & Explanation

Mitchel Aguirre

Mitchel Aguirre

Skilled2020-10-26Added 94 answers

We have to find the integral of: cos5(3x)sin2(3x)dx
Substitute u=3xdudx=3du3, we obtain cos5(3x)sin2(3x)dx=13cos5(3u)sin2(3u)du
Now solving: cos5(3u)sin2(3u)du=cos5(U)sin2(U)dU
Preparing for substitution, we use: cos2U=1sin2U, we obtain
Substitute v=sin(U)dvdU=cos(u)du=1cos(u)dv, we obtain:
Now, we can undo the substitution v=sin(u), we obtain:
Plug in solved integrals,

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