Integrating problems by hand

Question

Integrate.

Do this problem by hand (do not use the Table of Integrals).

Show all of your steps.

∫6sin3(𝑥)cos(𝑥)𝑑𝑥=  ?  + C

Which strategy did you choose?

u-Substitution

Partial Fractions

Trig substitution

integration by parts

algebraic manipulation / direct integration

Answer 1

See the video.

Answer 2

Use u-substitution with u = sinx. Then du = cosxdx.

6 ∫ sin³x cosx dx = 6 ∫ u³du = (3/2)u⁴ + C = (3/2)sin⁴x + C