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

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

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

\frac{3}{2} (z^{2} + 1)^{\frac{2}{3}} + C

Solution steps

Take the constant out:

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

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} u^{\frac{2}{3}}

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

Substitute back

u = z^{2} + 1

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

Simplify

2 \cdot \frac{1}{2} \cdot \frac{3}{2} (z^{2} + 1)^{\frac{2}{3}} : \frac{3}{2} (z^{2} + 1)^{\frac{2}{3}}

= \frac{3}{2} (z^{2} + 1)^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{2} (z^{2} + 1)^{\frac{2}{3}} + C

\frac{d}{d x} (e^{x^{2} - x + 1})

\frac{d}{d x} (x^{4} + 4 x^{3} - 2 x^{2} - 12 x)

\frac{d}{d x} (1 0^{- 2 x})

\int \frac{x ^{2}}{2 x - 1} d x

\frac{8}{( 9 s ^{2} + 12 s + 4 ) ( s )}

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