What is the integral of (1/(x^2)-4/(x^3)+2) ?

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

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integral of (1/(x^2)-4/(x^3)+2)

\int (\frac{1}{x ^{2}} - \frac{4}{x ^{3}} + 2) d x

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

Solution steps

\int \frac{1}{x ^{2}} - \frac{4}{x ^{3}} + 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 \frac{1}{x ^{2}} d x - \int \frac{4}{x ^{3}} d x + \int 2 d x

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

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

\int 2 d x = 2 x

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

Simplify

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

Add a constant to the solution

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

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