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

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

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integral of (2x^3)/(\sqrt[3]{x^4-5)}

\frac{3}{4} (x^{4} - 5)^{\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

: \int \frac{3 u}{4} d u

= 2 \cdot \int \frac{3 u}{4} d u

Take the constant out:

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

= 2 \cdot \frac{3}{4} \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 2 \cdot \frac{3}{4} \cdot \frac{u ^{2}}{2}

Substitute back

Simplify

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

Add a constant to the solution

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

ln (1 + x^{3})

\int - 5 csc^{2} (x) + 5 d x

\int (x e^{- x}) d x

\frac{\partial}{\partial y} (x y (x - 2) (y + 3))

x \to 0 lim (x^{2} + sin^{2} (x))

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