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

The integral of 3\sqrt[4]{x^3} is 12/7 x^{7/4}+C

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

\frac{12}{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

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

Apply the Power Rule

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

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

Simplify

3 \cdot \frac{4}{7} x^{\frac{7}{4}} : \frac{12}{7} x^{\frac{7}{4}}

= \frac{12}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{12}{7} x^{\frac{7}{4}} + C

\frac{\partial}{\partial x} (- 6 y^{6} sin (6 x))

\frac{d y}{d x} = 3 x^{2}

f (x) = \frac{3 - x}{x + 1}

\frac{d}{d x} (e^{- x} cos (5 x))

(8 \frac{1}{7}, 9), (4, 3.2)

What is the integral of 3\sqrt[4]{x^3} ?
The integral of 3\sqrt[4]{x^3} is 12/7 x^{7/4}+C