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

The integral of 1/((5x^1)^3) is -1/(250x^2)+C

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

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

- \frac{1}{250 x ^{2}} + C

Solution steps

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

Simplify

\frac{1}{( 5 x ^{1} ) ^{3}} : \frac{1}{125 x ^{3}}

= \int \frac{1}{125 x ^{3}} d x

Take the constant out:

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

= \frac{1}{125} \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

: - \frac{1}{2 x ^{2}}

= \frac{1}{125} (- \frac{1}{2 x ^{2}})

Simplify

\frac{1}{125} (- \frac{1}{2 x ^{2}}) : - \frac{1}{250 x ^{2}}

= - \frac{1}{250 x ^{2}}

Add a constant to the solution

= - \frac{1}{250 x ^{2}} + C

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What is the integral of 1/((5x^1)^3) ?
The integral of 1/((5x^1)^3) is -1/(250x^2)+C