Question

Integral desenvolvimento \int \:x^3\left(x^4-6\right)^7dx

Answer 1

Caso esteja pelo app, e tenha problemas para visualizar esta resposta, experimente abrir pelo navegador https://brainly.com.br/tarefa/38409537

                                             

$\displaystyle\sf\int x^3\cdot(x^4-6)^7~dx=\dfrac{1}{4}\int 4x^3\cdot(x^4-6)^7~dx\\\underline{\rm fac_{\!\!,}a}\\\sf u=x^4-6\implies du=4x^3~dx\\\displaystyle\sf\dfrac{1}{4}\int 4x^3\cdot(x^4-6)^7~dx=\dfrac{1}{4}\int u^7~du=\dfrac{1}{4}\cdot\dfrac{1}{8}u^8+k\\\displaystyle\sf\int u^7~du=\dfrac{1}{32}u^8+k\\\large\boxed{\boxed{\boxed{\boxed{\displaystyle\sf\int x^3\cdot(x^4-6)^7~dx=\dfrac{1}{32}(x^4-6)^8+k}}}}\blue{\checkmark}$