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

Add a constant to the solution

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

\frac{d}{d x} ((x^{4} + 2)^{2} (x^{3} + 4)^{4})

\int (e^{2 x} + e^{- 2 x}) d x

\frac{d}{d x} (3 (4 x^{2} + 3 x - 2)^{2})

\frac{5}{1 - 8 x}

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

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