Question

∫（1-cos^3x)dx答案是x-sinx+sin^3/3+c 还是x-sinx-sin^3/3+c

Answer 1

原式=∫1dx-∫cos^3x dx

=x+c-∫cos^2x d(sinx)

=x+c-∫(1-sin^2x)d(sinx)

=x+c-(sinx-sin^3x/3+c)

=x-sinx+sin^3/3+c