What is the integral of (27)/(x^4) ?

The integral of (27)/(x^4) is -9/(x^3)+C

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integral of (27)/(x^4)

\int \frac{27}{x ^{4}} d x

- \frac{9}{x ^{3}} + C

Solution steps

\int \frac{27}{x ^{4}} d x

Take the constant out:

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

= 27 \cdot \int \frac{1}{x ^{4}} d x

Apply the Power Rule

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

= 27 (- \frac{1}{3 x ^{3}})

Simplify

27 (- \frac{1}{3 x ^{3}}) : - \frac{9}{x ^{3}}

= - \frac{9}{x ^{3}}

Add a constant to the solution

= - \frac{9}{x ^{3}} + C

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