Question

这个不定积分

Answer 1

=(1/8)*∫(2sinx * cosx)^3 * dx

=(1/8)*∫[sin(2x)]^3 * dx

=(1/8)*∫[sin(2x)]^2 * sin(2x) * dx

=(1/8)*(1/2)*∫{1-[cos(2x)]^2} * [sin(2x) * d(2x)]

=(1/16)*∫[sin(2x)*d(2x)] - (1/16)*∫[cos(2x)]^2 * [sin(2x) * d(2x)]

=-(1/16)*cos(2x) + (1/16)*∫[cos(2x)]^2 * d[cos(2x)]

=-(1/16)*cos(2x) + (1/48)*[cos(2x)]^3 + C