What is the integral of (x+1)/(\sqrt[3]{x^2+2x+7)} ?

The integral of (x+1)/(\sqrt[3]{x^2+2x+7)} is 3/4 (x^2+2x+7)^{2/3}+C

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integral of (x+1)/(\sqrt[3]{x^2+2x+7)}

\frac{3}{4} (x^{2} + 2 x + 7)^{\frac{2}{3}} + C

Solution steps

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply the Power Rule

: \frac{3}{2} v^{\frac{2}{3}}

= \frac{1}{2} \cdot \frac{3}{2} v^{\frac{2}{3}}

Substitute back

= \frac{1}{2} \cdot \frac{3}{2} ((x + 1)^{2} + 6)^{\frac{2}{3}}

Simplify

\frac{1}{2} \cdot \frac{3}{2} ((x + 1)^{2} + 6)^{\frac{2}{3}} : \frac{3}{4} (x^{2} + 2 x + 7)^{\frac{2}{3}}

= \frac{3}{4} (x^{2} + 2 x + 7)^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{4} (x^{2} + 2 x + 7)^{\frac{2}{3}} + C

sin^{3} (2 x)

\frac{d}{d x} (\frac{2 x ^{2} + 6 x + 8}{x})

\frac{d}{d x} ((x^{2} + 5 x + 2)^{7})

\frac{\partial}{\partial z} (x y e^{x})

\frac{\partial}{\partial x} ((2 t - 1) (3 t - 6)^{- 1})

What is the integral of (x+1)/(\sqrt[3]{x^2+2x+7)} ?
The integral of (x+1)/(\sqrt[3]{x^2+2x+7)} is 3/4 (x^2+2x+7)^{2/3}+C