Question

calcule a integral x^5 ln x dx por partes

Answer 1

Boa noite Ana!

Solução!

$\boxed{ \int(udv)=uv-\int(vdu) }$

$v= x^{6}~~~~~~~~u=ln(x)\\\\ dv=6x^{5}~~~~~~du= \dfrac{1}{x}$


$\int(ln(x).6 x^{5})dx=ln(x). x^{6} -\int(x^{6}. \frac{1}{x})dx\\\\\\\ \int(ln(x).6 x^{5})dx=ln(x). x^{6}- \int(x^{5})dx\\\\\\\ \int(ln(x).6 x^{5})dx= \frac{1}{6}[ ln(x). x^{6}- \frac{ x^{6} }{6}]+c \\\\\\\\\\\ \boxed{Resposta: \dfrac{1}{6}ln(x). x^{6}- \dfrac{ x^{6} }{6}+c}$

Boa noite!
Bons estudos!