∫(x^3 )*(sin x^2) dx 求不定积分

题目

∫(x^3 )*(sin x^2) dx 求不定积分

答案

解
∫x³sinx²dx
=1/2∫x²sinx²dx²
=1/2∫usinudu
=-1/2∫ud(cosu)
=-1/2[ucosu-∫cosudu]
=-1/2ucosu+1/2sinu+C
=-1/2x²cosx²+1/2sinx²+C