What is the integral of 6x^{3/5} ?

The integral of 6x^{3/5} is 15/4 x^{8/5}+C

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integral of 6x^{3/5}

\int 6 x^{\frac{3}{5}} d x

\frac{15}{4} x^{\frac{8}{5}} + C

Solution steps

\int 6 x^{\frac{3}{5}} d x

Take the constant out:

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

= 6 \cdot \int x^{\frac{3}{5}} d x

Apply the Power Rule

: \frac{5}{8} x^{\frac{8}{5}}

= 6 \cdot \frac{5}{8} x^{\frac{8}{5}}

Simplify

6 \cdot \frac{5}{8} x^{\frac{8}{5}} : \frac{15}{4} x^{\frac{8}{5}}

= \frac{15}{4} x^{\frac{8}{5}}

Add a constant to the solution

= \frac{15}{4} x^{\frac{8}{5}} + C

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