Question

Ln 1 sobre x^2 dx seguindo a formula udv=u.v-/vdu

Answer 1

$\int\limits\dfrac{1}{x^2} \, dx \\\\u=x^2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,dv=dx\\u'=2xdx\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,v=x\\\\ \int\limits {udv}=uv- \int\limits {v} \, du\\\\=x^2.x- \int\limits {x.2x} \, dx \\\\=x^3-2\int{x^2}\,dx\\\\=x^3-2. \dfrac{x^3}{3} +C$

$= \dfrac{3x^3-2x^3}{3}+C\\\\ =\dfrac{x^3}{3}+C$