∫(3x+1)/(x^2+2x+17 )dx

题目

∫(3x+1)/(x^2+2x+17 )dx
太难了.T_T 请写出具体步骤,谢谢

答案

∫(3x+1)/(x^2+2x+17)dx
=3∫x/(x^2+2x+7)dx +∫1/(x^2+2x+17) dx
=3∫1/2*(2x+2-2) /(x^2+2x+17) dx+∫1/(x^2+2x+17)dx
=3/2*∫(2x+2)/(x^2+2x+17) dx -3∫1/(x^2+2x+17)dx +∫1/(x^2+2x+17) dx
=3/2 *∫1/(x^2+2x+17) d(x^2+2x+17) -2∫1/((x+1)^2+16) dx
=3/2*ln|x^2+2x+17| -2*1/4arctan(x+1)/4 +C
=3/2*ln|x^2+2x+17| -1/2*arctan((x+1)/4)+C
高数,5555
确实很难喔!
喵喵!