What is the integral of 1/x+2/(x^2)+10^x ?

The integral of 1/x+2/(x^2)+10^x is ln|x|-2/x+(10^x)/(ln(10))+C

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integral of 1/x+2/(x^2)+10^x

\int \frac{1}{x} + \frac{2}{x ^{2}} + 1 0^{x} d x

ln ∣ x ∣ - \frac{2}{x} + \frac{1 0 ^{x}}{ln ( 10 )} + C

Solution steps

\int \frac{1}{x} + \frac{2}{x ^{2}} + 1 0^{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{1}{x} d x + \int \frac{2}{x ^{2}} d x + \int 1 0^{x} d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

\int 1 0^{x} d x = \frac{1 0 ^{x}}{ln ( 10 )}

= ln ∣ x ∣ - \frac{2}{x} + \frac{1 0 ^{x}}{ln ( 10 )}

Add a constant to the solution

= ln ∣ x ∣ - \frac{2}{x} + \frac{1 0 ^{x}}{ln ( 10 )} + C

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What is the integral of 1/x+2/(x^2)+10^x ?
The integral of 1/x+2/(x^2)+10^x is ln|x|-2/x+(10^x)/(ln(10))+C