Question

Cum rezolv aceasta integrala?

Answer 1

Salut,

$\int_0^1\dfrac{x}{x^2+1}dx=\dfrac{1}2\cdot\int_0^1\dfrac{2x}{x^2+1}dx=\int_0^1\dfrac{1}{2}\left(\cdot (ln|x^2+1|\right)'dx=\\\\=\dfrac{1}2\cdot ln|x^2+1|\Big{|}_0^1=\dfrac{1}2\cdot ln(x^2+1)\Big{|}_0^1=\dfrac{1}2(ln2-ln1)=\dfrac{ln2}2.$

Green eyes.