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

x \to 5 - lim (\frac{( x + 1 )}{x - 5})

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

\frac{d}{d x} (- sin (x) - 2 cos (x))

\int (sin^{2} (x) cos^{3} (x)) d x

\frac{1}{s} \cdot \frac{1}{( s ^{2} + 3 s + 4 )}

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