What is the integral of (3x^2+14x-12+3/(x^2)) ?

The integral of (3x^2+14x-12+3/(x^2)) is x^3+7x^2-12x-3/x+C

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integral of (3x^2+14x-12+3/(x^2))

\int (3 x^{2} + 14 x - 12 + \frac{3}{x ^{2}}) d x

x^{3} + 7 x^{2} - 12 x - \frac{3}{x} + C

Solution steps

\int 3 x^{2} + 14 x - 12 + \frac{3}{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 3 x^{2} d x + \int 14 x d x - \int 12 d x + \int \frac{3}{x ^{2}} d x

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

\int 14 x d x = 7 x^{2}

\int 12 d x = 12 x

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

= x^{3} + 7 x^{2} - 12 x - \frac{3}{x}

Add a constant to the solution

= x^{3} + 7 x^{2} - 12 x - \frac{3}{x} + C

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What is the integral of (3x^2+14x-12+3/(x^2)) ?
The integral of (3x^2+14x-12+3/(x^2)) is x^3+7x^2-12x-3/x+C