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

The integral of ((3x^2+2)/(x^2)) is -(3x^2+2)/x+6x+C

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

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

- \frac{3 x ^{2} + 2}{x} + 6 x + C

Solution steps

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

Apply Integration By Parts

: - \frac{3 x ^{2} + 2}{x} - \int - 6 d x

= - \frac{3 x ^{2} + 2}{x} - \int - 6 d x

\int - 6 d x = - 6 x

= - \frac{3 x ^{2} + 2}{x} - (- 6 x)

Simplify

= - \frac{3 x ^{2} + 2}{x} + 6 x

Add a constant to the solution

= - \frac{3 x ^{2} + 2}{x} + 6 x + C

f (x) = x sin (x), 0, 2 π

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

f (x) = x - 5

y^{^{''}} + 2 y^{^{'}} + y = sin (x) + 4 cos (2 x)

(y + 4) \cdot \frac{d y}{d x} = 2 x y + 4 y

What is the integral of ((3x^2+2)/(x^2)) ?
The integral of ((3x^2+2)/(x^2)) is -(3x^2+2)/x+6x+C