What is the integral of (1/(x^2)+5/(sqrt(x))-1) ?

The integral of (1/(x^2)+5/(sqrt(x))-1) is -1/x+10sqrt(x)-x+C

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integral of (1/(x^2)+5/(sqrt(x))-1)

\int (\frac{1}{x ^{2}} + \frac{5}{x} - 1) d x

- \frac{1}{x} + 10 x - x + C

Solution steps

\int \frac{1}{x ^{2}} + \frac{5}{x} - 1 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 ^{2}} d x + \int \frac{5}{x} d x - \int 1 d x

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

\int \frac{5}{x} d x = 10 x

\int 1 d x = x

= - \frac{1}{x} + 10 x - x

Add a constant to the solution

= - \frac{1}{x} + 10 x - x + C

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What is the integral of (1/(x^2)+5/(sqrt(x))-1) ?
The integral of (1/(x^2)+5/(sqrt(x))-1) is -1/x+10sqrt(x)-x+C