Question

不定积分的小问题

求解答，虽然有参考答案但是有一步看不懂，希望有哥哥能书写一份尽可能详细的解答步骤，谢谢啦!

Answer 1

∫ x(lnx)^2 dx
=(1/2)∫ (lnx)^2 dx^2
=(1/2)x^2.(lnx)^2 - ∫ x(lnx) dx
=(1/2)x^2.(lnx)^2 -(1/2)∫ (lnx) dx^2
=(1/2)x^2.(lnx)^2 -(1/2)x^2.(lnx) +(1/2)∫ x dx
=(1/2)x^2.(lnx)^2 -(1/2)x^2.(lnx) +(1/4)x^2 +C