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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\int csc (8 x) d x

\int (5 e^{- x} - \frac{3}{2})^{2} d x

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

f (x) = 6 e^{x} + x, at x = 0

f (x) = 2 x x, at x = 1

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