Question

preciso de ajuda .......

Answer 1

Oi 

Integral por substituição:


$\int\limits {x(x^2+2)^3} \, dx \\ ---------------- \\ \boxed{u=x^2+2} ~~~~ \frac{du}{dx}=2x ~~~\boxed{dx= \frac{du}{2x} } \\ ---------------- \\ \int\limits {x(u)^3} \, \frac{du}{2x} \\ \\ \frac{1}{2} \int\limits {(u)^3} \, du \\ \\ \frac{1}{2} \frac{u^{3+1}}{3+1}+C \\ \\ \frac{1}{2} \frac{u^{4}}{4}+C \\ \\ \boxed{\frac{1}{8}(x^2+2)^4+C }$