What is the integral of 5x^{3/7} ?

The integral of 5x^{3/7} is 7/2 x^{10/7}+C

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integral of 5x^{3/7}

\int 5 x^{\frac{3}{7}} d x

\frac{7}{2} x^{\frac{10}{7}} + C

Solution steps

\int 5 x^{\frac{3}{7}} d x

Take the constant out:

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

= 5 \cdot \int x^{\frac{3}{7}} d x

Apply the Power Rule

= 5 \cdot \frac{7}{10} x^{\frac{10}{7}}

Simplify

5 \cdot \frac{7}{10} x^{\frac{10}{7}} : \frac{7}{2} x^{\frac{10}{7}}

= \frac{7}{2} x^{\frac{10}{7}}

Add a constant to the solution

= \frac{7}{2} x^{\frac{10}{7}} + C