Question

高数题😭大神帮帮忙吧

高数题😭大神帮帮忙吧那一步是怎么算的啊

Answer 1

∫1dx/(1+x)
=∫d(1+x)/(1+x)
=ln(1+x)
∫(1-x)dx/(1+x²)
=∫dx/(1+x²)-∫xdx/(1+x²)
=arctanx-(1/2)∫d(1+x²)/(1+x²)
=arctanx-(1/2)ln(1+x²)
ln(1+x)-(1/2)ln(1+x²)
=ln[(1+x)/(1+x²)^{1/2}]
=ln[(1+x)²/(1+x²)]