What is the integral of 6x^{2/5} ?

The integral of 6x^{2/5} is 30/7 x^{7/5}+C

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integral of 6x^{2/5}

\int 6 x^{\frac{2}{5}} d x

\frac{30}{7} x^{\frac{7}{5}} + C

Solution steps

\int 6 x^{\frac{2}{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{2}{5}} d x

Apply the Power Rule

: \frac{5}{7} x^{\frac{7}{5}}

= 6 \cdot \frac{5}{7} x^{\frac{7}{5}}

Simplify

6 \cdot \frac{5}{7} x^{\frac{7}{5}} : \frac{30}{7} x^{\frac{7}{5}}

= \frac{30}{7} x^{\frac{7}{5}}

Add a constant to the solution

= \frac{30}{7} x^{\frac{7}{5}} + C

tan (5 x)

\frac{2}{4 ( s - 3 ) ^{2} + 64}

\int cos^{4} (5 x + 1) d x

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\int arctan (2 x) d x