What is the integral of (4/(x^3)) ?

The integral of (4/(x^3)) is -2/(x^2)+C

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integral of (4/(x^3))

\int (\frac{4}{x ^{3}}) d x

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

Solution steps

\int \frac{4}{x ^{3}} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

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

= 4 (- \frac{1}{2 x ^{2}})

Simplify

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x ^{2} + 2}{x - 1})

f (x) = (x - 2)^{3} + 10

\int (3 x^{2} + 2) 2 x^{3} + 4 x + 1 d x

f (x) = ln (x e^{- 3 x})

\int \frac{1}{x ln ( 2 x )} d x