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Popular Calculus >

integral of (2+3^x)

Solution

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

Solution

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

Solution steps

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

\int 2 d x = 2 x

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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