What is the integral of (2x^1)/((x^5)^3) ?

The integral of (2x^1)/((x^5)^3) is -2/(13x^{13)}+C

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integral of (2x^1)/((x^5)^3)

\int \frac{2 x ^{1}}{( x ^{5} ) ^{3}} d x

- \frac{2}{13 x ^{13}} + C

Solution steps

\int \frac{2 x ^{1}}{( x ^{5} ) ^{3}} d x

Take the constant out:

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

= 2 \cdot \int \frac{x ^{1}}{( x ^{5} ) ^{3}} d x

Simplify

\frac{x ^{1}}{( x ^{5} ) ^{3}} : \frac{1}{x ^{14}}

= 2 \cdot \int \frac{1}{x ^{14}} d x

Apply the Power Rule

: - \frac{1}{13 x ^{13}}

= 2 (- \frac{1}{13 x ^{13}})

Simplify

2 (- \frac{1}{13 x ^{13}}) : - \frac{2}{13 x ^{13}}

= - \frac{2}{13 x ^{13}}

Add a constant to the solution

= - \frac{2}{13 x ^{13}} + C

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What is the integral of (2x^1)/((x^5)^3) ?
The integral of (2x^1)/((x^5)^3) is -2/(13x^{13)}+C