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

The integral of (2/(x^3)+3/(x^2)+3^x) is -1/(x^2)-3/x+(3^x)/(ln(3))+C

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

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

- \frac{1}{x ^{2}} - \frac{3}{x} + \frac{3 ^{x}}{ln ( 3 )} + C

Solution steps

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

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

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

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

= - \frac{1}{x ^{2}} - \frac{3}{x} + \frac{3 ^{x}}{ln ( 3 )}

Add a constant to the solution

= - \frac{1}{x ^{2}} - \frac{3}{x} + \frac{3 ^{x}}{ln ( 3 )} + C

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What is the integral of (2/(x^3)+3/(x^2)+3^x) ?
The integral of (2/(x^3)+3/(x^2)+3^x) is -1/(x^2)-3/x+(3^x)/(ln(3))+C