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

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

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

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

- \frac{1}{x} + \frac{2}{x} + 5 x + C

Solution steps

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

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

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

\int 5 d x = 5 x

= - \frac{1}{x} - (- \frac{2}{x}) + 5 x

Simplify

= - \frac{1}{x} + \frac{2}{x} + 5 x

Add a constant to the solution

= - \frac{1}{x} + \frac{2}{x} + 5 x + C

4 x sin (x)

- 4 y^{^{'}} + 12 x^{2} = 0

\frac{\partial}{\partial x} (3 y^{2} cos (5 x))

\frac{\partial}{\partial x} (2 x y e^{x y^{2}} - 3 y^{2})

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

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