What is the integral of 2sqrt(x)-x-9/(x^2) ?

The integral of 2sqrt(x)-x-9/(x^2) is 4/3 x^{3/2}-(x^2)/2+9/x+C

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integral of 2sqrt(x)-x-9/(x^2)

\int 2 x - x - \frac{9}{x ^{2}} d x

\frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + \frac{9}{x} + C

Solution steps

\int 2 x - x - \frac{9}{x ^{2}} 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 2 x d x - \int x d x - \int \frac{9}{x ^{2}} d x

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

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

\int \frac{9}{x ^{2}} d x = - \frac{9}{x}

= \frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} - (- \frac{9}{x})

Simplify

= \frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + \frac{9}{x}

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + \frac{9}{x} + C

What is the integral of 2sqrt(x)-x-9/(x^2) ?
The integral of 2sqrt(x)-x-9/(x^2) is 4/3 x^{3/2}-(x^2)/2+9/x+C