Question

不定积分xf（x^2)f'(x^2)dx=多少 要详细过程

Answer 1

凑一下就可以，因为df(x^2)=2xf'(x^2)
所以∫xf(x^2)f'(x^2)dx
=1/2∫[2xf'(x^2)]*f(x^2)dx
=1/2∫f(x^2)df(x^2)
=1/2*1/2*[f(x^2)]^2+C
=1/4*[f(x^2)]^2+C
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