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

The integral of (3+2x^2)/(x^2) is -3/x+2x+C

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

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

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

Solution steps

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

Expand

\frac{3 + 2 x ^{2}}{x ^{2}} : \frac{3}{x ^{2}} + 2

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{10}{x ^{3}})

\frac{7}{4 s - 12}

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

\frac{d}{d x} (\frac{π}{x ^{18}})

f (x) = 2 x^{3} - 6 x, at x = - 3

What is the integral of (3+2x^2)/(x^2) ?
The integral of (3+2x^2)/(x^2) is -3/x+2x+C