∫{（x+1）^2/[x(x^2+1)]}dx=A.ln|x|+x+C B.ln|x|+ln(1+x^2)+CC.ln|x|+2arctanx+C D.ln|x|+C
问题描述：
∫{（x+1）^2/[x(x^2+1)]}dx=
A.ln|x|+x+C B.ln|x|+ln(1+x^2)+C
C.ln|x|+2arctanx+C D.ln|x|+C
答
∫{(x+1)²/[x(x²+1)]}dx
=∫{(x²+2x+1)/[x(x²+1)]}dx
=∫[(1/x)+2/(x²+1)]dx
=∫(1/x)dx+2∫[1/(x²+1)]dx
=ln|x|+2arctanx+C
选C
答
∫{（x+1）^2/[x(x^2+1)]}dx
=∫{（x^2+1+2x）/[x(x^2+1)]}dx
=∫1/xdx+∫2/(x^2+1)dx
=.ln|x|+2arctanx+C
选C