What is the integral of 7/8 x^{7/8} ?

The integral of 7/8 x^{7/8} is 7/15 x^{15/8}+C

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integral of 7/8 x^{7/8}

\int \frac{7}{8} x^{\frac{7}{8}} d x

\frac{7}{15} x^{\frac{15}{8}} + C

Solution steps

\int \frac{7}{8} x^{\frac{7}{8}} d x

Take the constant out:

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

= \frac{7}{8} \cdot \int x^{\frac{7}{8}} d x

Apply the Power Rule

: \frac{8}{15} x^{\frac{15}{8}}

= \frac{7}{8} \cdot \frac{8}{15} x^{\frac{15}{8}}

Simplify

\frac{7}{8} \cdot \frac{8}{15} x^{\frac{15}{8}} : \frac{7}{15} x^{\frac{15}{8}}

= \frac{7}{15} x^{\frac{15}{8}}

Add a constant to the solution

= \frac{7}{15} x^{\frac{15}{8}} + C

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What is the integral of 7/8 x^{7/8} ?
The integral of 7/8 x^{7/8} is 7/15 x^{15/8}+C