Question

∫x(x-6)³dx by using substitution u=x-6​

Answer 1

`\large\boxed{\int\bigg(x(x-6)^3\bigg)dx=(1)/(5)(x-6)^5+(3)/(2)(x-6)^4+C}`

Explanation:

`\int\bigg(x(x-6)^3\bigg)dx\Rightarrow\left[\begin{array}{ccc}x-6=u\\x=u+6\\dx=du\end{array}\right]\Rightarrow\int\bigg((u+6)u^3\bigg)du\\\\=\int(u^4+6u^3)du=(1)/(5)u^5+(6)/(4)u^4+C=(1)/(5)(x-6)^5+(3)/(2)(x-6)^4+C`