What is the integral of (2/(x^6)) ?

The integral of (2/(x^6)) is -2/(5x^5)+C

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integral of (2/(x^6))

\int (\frac{2}{x ^{6}}) d x

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

Solution steps

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

Take the constant out:

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

= 2 \cdot \int \frac{1}{x ^{6}} d x

Apply the Power Rule

= 2 (- \frac{1}{5 x ^{5}})

Simplify

2 (- \frac{1}{5 x ^{5}}) : - \frac{2}{5 x ^{5}}

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

Add a constant to the solution

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