What is the integral of x^5+8x^{-3}+2 ?

The integral of x^5+8x^{-3}+2 is (x^6)/6-4/(x^2)+2x+C

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integral of x^5+8x^{-3}+2

\int x^{5} + 8 x^{- 3} + 2 d x

\frac{x ^{6}}{6} - \frac{4}{x ^{2}} + 2 x + C

Solution steps

\int x^{5} + 8 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 x^{5} d x + \int 8 x^{- 3} d x + \int 2 d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 8 x^{- 3} d x = - \frac{4}{x ^{2}}

\int 2 d x = 2 x

= \frac{x ^{6}}{6} - \frac{4}{x ^{2}} + 2 x

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{4}{x ^{2}} + 2 x + C

\frac{d}{d x} (3 x^{3} + 5 x)

\frac{\partial}{\partial x} (x y - ln (z))

\int e^{x + y} d y

\frac{\partial}{\partial s} (\frac{s ^{2} + 4}{t - 3})

x \to 0 - lim (\frac{2 x}{∣ x ∣})

What is the integral of x^5+8x^{-3}+2 ?
The integral of x^5+8x^{-3}+2 is (x^6)/6-4/(x^2)+2x+C