Question

微积分。。不定积分。。自然对数。。求解！！！

Answer 1

原式=xln(x^2+15x+54)-2∫x^2/(x^2+15x+54)dx
=xln(x^2+15x+54)-2∫{1-(15x+54)/[(x+6)(x+9)]}dx
=xln(x^2+15x+54)-2x+∫(15x+54)/[(x+6)(x+9)]dx
=xln(x^2+15x+54)-2x-12∫dx/(x+6)-27∫dx/(x+9)
=xln(x^2+15x+54)-2x-12ln|x+6|-27ln|x+9|+C

Answer 2

你把（x^2+15x+54）分解后，再拆开为ln(x+6)+ln(x+9),后边你懂得了！