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

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

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

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

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

Solution steps

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

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

\int \frac{1}{x} d x = 2 x

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

Add a constant to the solution

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

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