What is the integral of (5x\sqrt[4]{6x^2+5})/4 ?

The integral of (5x\sqrt[4]{6x^2+5})/4 is 1/12 (6x^2+5)^{5/4}+C

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integral of (5x\sqrt[4]{6x^2+5})/4

\frac{1}{12} (6 x^{2} + 5)^{\frac{5}{4}} + 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{4}{5} u^{\frac{5}{4}}

= \frac{5}{4} \cdot \frac{1}{12} \cdot \frac{4}{5} u^{\frac{5}{4}}

Substitute back

u = 6 x^{2} + 5

= \frac{5}{4} \cdot \frac{1}{12} \cdot \frac{4}{5} (6 x^{2} + 5)^{\frac{5}{4}}

Simplify

\frac{5}{4} \cdot \frac{1}{12} \cdot \frac{4}{5} (6 x^{2} + 5)^{\frac{5}{4}} : \frac{1}{12} (6 x^{2} + 5)^{\frac{5}{4}}

= \frac{1}{12} (6 x^{2} + 5)^{\frac{5}{4}}

Add a constant to the solution

= \frac{1}{12} (6 x^{2} + 5)^{\frac{5}{4}} + C

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What is the integral of (5x\sqrt[4]{6x^2+5})/4 ?
The integral of (5x\sqrt[4]{6x^2+5})/4 is 1/12 (6x^2+5)^{5/4}+C