What is the integral of 3/(x^2)+4sqrt(x) ?

The integral of 3/(x^2)+4sqrt(x) is -3/x+8/3 x^{3/2}+C

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integral of 3/(x^2)+4sqrt(x)

\int \frac{3}{x ^{2}} + 4 x d x

- \frac{3}{x} + \frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{3}{x ^{2}} + 4 x 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{3}{x ^{2}} d x + \int 4 x d x

\int \frac{3}{x ^{2}} d x = - \frac{3}{x}

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

= - \frac{3}{x} + \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= - \frac{3}{x} + \frac{8}{3} x^{\frac{3}{2}} + C

y^{2} d x - x y d y = x^{2} y d y

\frac{1}{2} x^{2}, x^{2} - 3 x

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

x \to 0 lim (- e^{\frac{1}{x}})

x \to 2 lim (\frac{x ^{2} - 1}{x + 1})

What is the integral of 3/(x^2)+4sqrt(x) ?
The integral of 3/(x^2)+4sqrt(x) is -3/x+8/3 x^{3/2}+C