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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

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

\int tan (x - 7) \frac{1}{x - 7} d x

\int e^{a x + 7} d x

\frac{\partial}{\partial y} (- x)

f (x) = x^{4} - 17 x^{2} + 16, at x = 1

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