What is the integral of 2x^{(-3)/5} ?

The integral of 2x^{(-3)/5} is 5x^{2/5}+C

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integral of 2x^{(-3)/5}

\int 2 x^{\frac{- 3}{5}} d x

5 x^{\frac{2}{5}} + C

Solution steps

\int 2 x^{\frac{- 3}{5}} d x

Take the constant out:

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

= 2 \cdot \int x^{\frac{- 3}{5}} d x

Apply the Power Rule

: \frac{5}{2} x^{\frac{2}{5}}

= 2 \cdot \frac{5}{2} x^{\frac{2}{5}}

Simplify

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

= 5 x^{\frac{2}{5}}

Add a constant to the solution

= 5 x^{\frac{2}{5}} + C

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