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

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

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

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

- \frac{1}{x ^{2}} + 2 x - 4 arcsin (x) + C

Solution steps

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

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

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

\int \frac{4}{1 - x ^{2}} d x = 4 arcsin (x)

= - \frac{1}{x ^{2}} + 2 x - 4 arcsin (x)

Add a constant to the solution

= - \frac{1}{x ^{2}} + 2 x - 4 arcsin (x) + C

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