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Popular Calculus >

integral of 3^x+2/x

Solution

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

Solution

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

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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