What is the integral of (1/(5x^4)) ?

The integral of (1/(5x^4)) is -1/(15x^3)+C

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integral of (1/(5x^4))

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

- \frac{1}{15 x ^{3}} + C

Solution steps

\int \frac{1}{5 x ^{4}} d x

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{x ^{4}} d x

Apply the Power Rule

: - \frac{1}{3 x ^{3}}

= \frac{1}{5} (- \frac{1}{3 x ^{3}})

Simplify

\frac{1}{5} (- \frac{1}{3 x ^{3}}) : - \frac{1}{15 x ^{3}}

= - \frac{1}{15 x ^{3}}

Add a constant to the solution

= - \frac{1}{15 x ^{3}} + C

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