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

\frac{d}{d x} (\frac{3 x}{x ^{2} - 1})

\frac{d}{d x} (\frac{5 x - 4}{3 x ^{2} + 1})

y^{^{''}} + 6 y^{^{'}} + 34 y = 0, y (0) = - 1, y^{^{'}} (0) = 13

f (x) = \frac{28}{x}

x \to 1 lim (2 x + 1)

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