t*sin^3(t) dt.求积分啊.

Question

t*sin^3(t) dt.求积分啊.

Answer 1

sin^3(t) = [1-cos(2t)] sint / 2 = (3/4)sint - (1/4) sin(3t)
I = (3/4) ∫ t d(-cost) + (1/12) ∫ t d(cos3t)
= (-3/4) [ t cost - ∫ cost dt ] + (1/12) [ t cos(3t) - ∫ cos(3t) dt ]
= (-3/4) [ t cost - sint] + (1/12) [ t cos(3t) - (1/3) sin(3t) ] + C