What is the integral of (8x^3+2/(x^2)) ?

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

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integral of (8x^3+2/(x^2))

\int (8 x^{3} + \frac{2}{x ^{2}}) d x

2 x^{4} - \frac{2}{x} + C

Solution steps

\int 8 x^{3} + \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 8 x^{3} d x + \int \frac{2}{x ^{2}} d x

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

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

= 2 x^{4} - \frac{2}{x}

Add a constant to the solution

= 2 x^{4} - \frac{2}{x} + C

\int (8 e^{x}) d x

\int (\frac{3}{4} x - \frac{2}{5})^{2} d x

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

\int \frac{( x - 1 ) ^{2}}{x ^{2} - 5 x + 6} d x

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