Question

Помогите решить дальше

Answer 1

t=x^2

dt=2xdx; xdx=dt/2

0.5∫dt/(t-1)=0.5ln|t-1|=0.5ln|x^2-1|=0.5ln8-0.5ln1=0.5ln8

Answer 2

$\int\limits^3_{\sqrt{2}} {\frac{x}{x^2-1}} \, dx =\int\limits^3_{\sqrt{2}} {\frac{1}{2(x^2-1)}} \, d(x^2-1)=\\=0,5ln(x^2-1)|^3_{\sqrt{2}}=0,5(ln8 - ln1) = 1,5ln2$