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

The integral of (4x+3x^2-2/(x^2)) is 2x^2+x^3+2/x+C

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

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

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

Solution steps

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

\int 4 x d x = 2 x^{2}

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

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

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

Simplify

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

Add a constant to the solution

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

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\int \frac{1}{7 x + 11} d x

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