What is the integral of 1/(x^2)+4/(xsqrt(x))+2 ?

The integral of 1/(x^2)+4/(xsqrt(x))+2 is -1/x-8/(sqrt(x))+2x+C

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integral of 1/(x^2)+4/(xsqrt(x))+2

\int \frac{1}{x ^{2}} + \frac{4}{x x} + 2 d x

- \frac{1}{x} - \frac{8}{x} + 2 x + C

Solution steps

\int \frac{1}{x ^{2}} + \frac{4}{x x} + 2 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{4}{x x} d x + \int 2 d x

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

\int \frac{4}{x x} d x = - \frac{8}{x}

\int 2 d x = 2 x

= - \frac{1}{x} - \frac{8}{x} + 2 x

Add a constant to the solution

= - \frac{1}{x} - \frac{8}{x} + 2 x + C

\int x e^{y} d y

\frac{d}{d t} (a e^{t})

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

4 x^{2} y d x + x y d y = 0

\int_{0}^{5} t e^{- t} d t

What is the integral of 1/(x^2)+4/(xsqrt(x))+2 ?
The integral of 1/(x^2)+4/(xsqrt(x))+2 is -1/x-8/(sqrt(x))+2x+C