What is the integral of 3x^2\sqrt[3]{2x^3+5} ?

The integral of 3x^2\sqrt[3]{2x^3+5} is 3/8 (2x^3+5)^{4/3}+C

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integral of 3x^2\sqrt[3]{2x^3+5}

\frac{3}{8} (2 x^{3} + 5)^{\frac{4}{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}{4} u^{\frac{4}{3}}

= 3 \cdot \frac{1}{6} \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = 2 x^{3} + 5

= 3 \cdot \frac{1}{6} \cdot \frac{3}{4} (2 x^{3} + 5)^{\frac{4}{3}}

Simplify

3 \cdot \frac{1}{6} \cdot \frac{3}{4} (2 x^{3} + 5)^{\frac{4}{3}} : \frac{3}{8} (2 x^{3} + 5)^{\frac{4}{3}}

= \frac{3}{8} (2 x^{3} + 5)^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{8} (2 x^{3} + 5)^{\frac{4}{3}} + C

\frac{\partial}{\partial s} (3 s^{2} + t^{2})

\frac{d y}{d x} = x - y, y (0) = 2

x \to 0 lim (ln (\frac{1}{x ^{2}}))

\frac{\partial}{\partial z} (y^{2} z)

\int_{0}^{N} e^{- s t} cos (3 t) d t

What is the integral of 3x^2\sqrt[3]{2x^3+5} ?
The integral of 3x^2\sqrt[3]{2x^3+5} is 3/8 (2x^3+5)^{4/3}+C