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

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

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

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

\frac{x ^{4}}{2} - \frac{3}{x} + 8 e^{x} + C

Solution steps

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

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

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

\int 8 e^{x} d x = 8 e^{x}

= \frac{x ^{4}}{2} - \frac{3}{x} + 8 e^{x}

Add a constant to the solution

= \frac{x ^{4}}{2} - \frac{3}{x} + 8 e^{x} + C

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