求不定积分f x/(1+x^2)dx

问题描述:

求不定积分f x/(1+x^2)dx

∫x/(1+x∧2)dx
=1/2∫d(1+x∧2)/(1+x∧2)
=1/2 ln(1+x∧2) +c

f x/(1+x^2)dx=(1/2)*∫1/(1+x²)dx²
=(1/2)*∫1/(1+x²)d(x²+1)
=(1/2)*ln(x²+1)+C (C为常数)