Question

calcule a integral ʃ x/(x²+10)³ dx

Answer 1

$\int\limits \frac{x}{(x^2+10)^3} dx \\ \\ x^2+10=u=\ \textgreater \ 2xdx=du=\ \textgreater \ xdx= \frac{1}{2} du \\ \int\limits \frac{ \frac{1}{2} }{u^3} du= \frac{1}{2} \int\limits u^-^3du= \frac{1}{2} . \frac{u^-^2}{-2} =- \frac{1}{4}. \frac{1}{u^2} +c=- \frac{1}{4(x^2+10)^3} +c$