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

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

\int_{- 5}^{5} (4 - ∣ x ∣) d x

y = 8 csc (2 x^{4} - 7 x + 3)

\frac{d}{d x} (5 x^{5} f (x))

y^{^{'}} = e^{t + y}, y (0) = 0

\int 5 e^{3 x + 7} d x

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