What is the integral of (15)/(x^4) ?

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

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integral of (15)/(x^4)

\int \frac{15}{x ^{4}} d x

- \frac{5}{x ^{3}} + C

Solution steps

\int \frac{15}{x ^{4}} d x

Take the constant out:

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

= 15 \cdot \int \frac{1}{x ^{4}} d x

Apply the Power Rule

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

Simplify

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

= - \frac{5}{x ^{3}}

Add a constant to the solution

= - \frac{5}{x ^{3}} + C