Integrating problems by hand

Question

Integrate.

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

∫16𝑥sin(𝑥)𝑑𝑥=  ?  + C

Which strategy did you choose?

u-Substitution

Partial Fractions

Trig substitution

integration by parts

algebraic manipulation / direct integration

Answer 1

Answer 2

Use integration by parts with u = x and dv = sinxdx. So, du = dx and v = ∫dv = -cosx.

16 ∫ xsinxdx = 16 (uv - ∫vdu ) = 16(-xcosx + ∫cosxdx) = -16xcosx + 16sinx + C