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

The integral of (3\sqrt[4]{x^5})/4 is 1/3 x^{9/4}+C

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

\int \frac{3 4 x ^{5}}{4} d x

\frac{1}{3} x^{\frac{9}{4}} + C

Solution steps

\int \frac{3 4 x ^{5}}{4} d x

Take the constant out:

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

= \frac{3}{4} \cdot \int 4 x^{5} d x

4 x^{5} = x^{\frac{5}{4}},

assuming

x \geq 0

= \frac{3}{4} \cdot \int x^{\frac{5}{4}} d x

Apply the Power Rule

= \frac{3}{4} \cdot \frac{4}{9} x^{\frac{9}{4}}

Simplify

\frac{3}{4} \cdot \frac{4}{9} x^{\frac{9}{4}} : \frac{1}{3} x^{\frac{9}{4}}

= \frac{1}{3} x^{\frac{9}{4}}

Add a constant to the solution

= \frac{1}{3} x^{\frac{9}{4}} + C

\int 3 - 0.01 x + 0.000006 x^{2} d x

\int \frac{x ^{2} + 6 x + 4}{x ^{3} + 9 x ^{2} + 12 x + 1} d x

\int 10 x^{2} sin (2 x) d x

\int 18 e^{x} sin (x) d x

\int e^{x - x^{2}} d x

What is the integral of (3\sqrt[4]{x^5})/4 ?
The integral of (3\sqrt[4]{x^5})/4 is 1/3 x^{9/4}+C