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

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

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

\frac{3}{4} (x^{2} + 1)^{\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} u^{\frac{2}{3}}

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

Substitute back

u = x^{2} + 1

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

Simplify

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

= \frac{3}{4} (x^{2} + 1)^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{4} (x^{2} + 1)^{\frac{2}{3}} + C

\int \frac{1}{484 + x ^{2}} d x

5 \frac{d y}{d x} + 45 y = 9

\frac{d}{d x} (x^{2} cos (y) y^{^{'}})

f (x) = 2 cos (3 x)

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

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