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Step-by-step Solution

Integrate 1/((x+1)^(1/3)) from -1 to 7

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Answer

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

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

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

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Answer

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

Main topic:

Integral calculus

Used formulas:

3. See formulas

Time to solve it:

~ 0.63 seconds