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

The integral of (3\sqrt[4]{x^3})/4 is 3/7 x^{7/4}+C

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

\frac{3}{7} x^{\frac{7}{4}} + C

Solution steps

Take the constant out:

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

assuming

x \geq 0

= \frac{3}{4} \cdot \int x^{\frac{3}{4}} d x

Apply the Power Rule

= \frac{3}{4} \cdot \frac{4}{7} x^{\frac{7}{4}}

Simplify

\frac{3}{4} \cdot \frac{4}{7} x^{\frac{7}{4}} : \frac{3}{7} x^{\frac{7}{4}}

= \frac{3}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{3}{7} x^{\frac{7}{4}} + C

What is the integral of (3\sqrt[4]{x^3})/4 ?
The integral of (3\sqrt[4]{x^3})/4 is 3/7 x^{7/4}+C