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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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

\int - \frac{24}{x ^{25}} d x

\int r^{2} + 1 d r

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

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