What is the integral of 8x^{3/4} ?

The integral of 8x^{3/4} is 32/7 x^{7/4}+C

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integral of 8x^{3/4}

\int 8 x^{\frac{3}{4}} d x

\frac{32}{7} x^{\frac{7}{4}} + C

Solution steps

\int 8 x^{\frac{3}{4}} d x

Take the constant out:

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

= 8 \cdot \int x^{\frac{3}{4}} d x

Apply the Power Rule

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

= 8 \cdot \frac{4}{7} x^{\frac{7}{4}}

Simplify

8 \cdot \frac{4}{7} x^{\frac{7}{4}} : \frac{32}{7} x^{\frac{7}{4}}

= \frac{32}{7} x^{\frac{7}{4}}

Add a constant to the solution

= \frac{32}{7} x^{\frac{7}{4}} + C

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