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

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

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

\int (3 x - 2 x^{- 3}) d x

2 x^{\frac{3}{2}} + \frac{1}{x ^{2}} + C

Solution steps

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

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

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

= 2 x^{\frac{3}{2}} - (- \frac{1}{x ^{2}})

Simplify

= 2 x^{\frac{3}{2}} + \frac{1}{x ^{2}}

Add a constant to the solution

= 2 x^{\frac{3}{2}} + \frac{1}{x ^{2}} + C

\frac{π x}{2}

\int \frac{5}{x} - \frac{10}{x ^{2}} d x

\frac{d}{d x} ((x^{3} - 2 x + 1) (3 x^{3} + 2 x^{2} - 5 x))

x \to - \infty lim (\frac{x}{- 1})

\frac{\partial}{\partial y} (e^{y x} y^{2})

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