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

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

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integral of 1/(sqrt(x))-2/(sqrt(x^3))

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

2 x + \frac{4}{x} + C

Solution steps

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

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

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

= 2 x - (- \frac{4}{x})

Simplify

= 2 x + \frac{4}{x}

Add a constant to the solution

= 2 x + \frac{4}{x} + C

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