Step-by-step Solution

Integrate $\frac{1}{\left(x+1\right)^{\left(\frac{1}{3}\right)}}$ from $-1$ to $7$

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$6$

Step-by-step explanation

Problem to solve:

$\int_{-1}^7\left(\frac{1}{\left(X+1\right)^{\frac{1}{3}}}\right)dx$
1

Solve the integral $\int_{-1}^{7}\frac{1}{\sqrt[3]{x+1}}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x+1 \\ du=dx\end{matrix}$
2

Substituting $u$ and $dx$ in the integral and simplify

$\int_{-1}^{7}\frac{1}{\sqrt[3]{u}}du$

$6$
$\int_{-1}^7\left(\frac{1}{\left(X+1\right)^{\frac{1}{3}}}\right)dx$

Main topic:

Definite integrals

~ 0.98 seconds