What is the integral of (1+2/(x^2)+3/(x^3)) ?

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

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integral of (1+2/(x^2)+3/(x^3))

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

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

Solution steps

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

\int 1 d x = x

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

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

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

Add a constant to the solution

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

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