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

Popular >

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

\frac{d y}{d x} = 3 y e^{x + 7}

\int - \frac{cos ( x )}{x} d x

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{- x}

y = x^{2} - 15, y = 1

(x, y) \to (0, 1) lim (\frac{e ^{x y}}{x + 1})

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