What is the integral of 2/(x^{-3)}-1/(sqrt(x^3)) ?

The integral of 2/(x^{-3)}-1/(sqrt(x^3)) is (x^4)/2+2/(sqrt(x))+C

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integral of 2/(x^{-3)}-1/(sqrt(x^3))

\int \frac{2}{x ^{- 3}} - \frac{1}{x ^{3}} d x

\frac{x ^{4}}{2} + \frac{2}{x} + C

Solution steps

\int \frac{2}{x ^{- 3}} - \frac{1}{x ^{3}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2}{x ^{- 3}} d x - \int \frac{1}{x ^{3}} d x

\int \frac{2}{x ^{- 3}} d x = \frac{x ^{4}}{2}

\int \frac{1}{x ^{3}} d x = - \frac{2}{x}

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

Simplify

= \frac{x ^{4}}{2} + \frac{2}{x}

Add a constant to the solution

= \frac{x ^{4}}{2} + \frac{2}{x} + C

x \to 2 lim (\frac{1}{x ^{3}})

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What is the integral of 2/(x^{-3)}-1/(sqrt(x^3)) ?
The integral of 2/(x^{-3)}-1/(sqrt(x^3)) is (x^4)/2+2/(sqrt(x))+C