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

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

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integral of (x^2+x+x^{-3})

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

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}} + C

Solution steps

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

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

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

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

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}} + C

\frac{d}{d x} (\frac{x}{x ^{2} - 9})

\int \frac{1}{64 e ^{- 7 x} + e ^{7 x}} d x

x \to 0 lim (\frac{5}{x + x ^{2}})

f (x) = 10 x + 6

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

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