What is the integral of (x^{3+1/7})/7 ?

The integral of (x^{3+1/7})/7 is 1/29 x^{29/7}+C

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integral of (x^{3+1/7})/7

\int \frac{x ^{3 + \frac{1}{7}}}{7} d x

\frac{1}{29} x^{\frac{29}{7}} + C

Solution steps

\int \frac{x ^{3 + \frac{1}{7}}}{7} d x

Take the constant out:

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

= \frac{1}{7} \cdot \int x^{3 + \frac{1}{7}} d x

Apply the Power Rule

: \frac{7}{29} x^{\frac{29}{7}}

= \frac{1}{7} \cdot \frac{7}{29} x^{\frac{29}{7}}

Simplify

\frac{1}{7} \cdot \frac{7}{29} x^{\frac{29}{7}} : \frac{1}{29} x^{\frac{29}{7}}

= \frac{1}{29} x^{\frac{29}{7}}

Add a constant to the solution

= \frac{1}{29} x^{\frac{29}{7}} + C

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What is the integral of (x^{3+1/7})/7 ?
The integral of (x^{3+1/7})/7 is 1/29 x^{29/7}+C