What is the integral of (5/x+4^x) ?

The integral of (5/x+4^x) is 5ln|x|+(2^{2x-1})/(ln(2))+C

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integral of (5/x+4^x)

\int (\frac{5}{x} + 4^{x}) d x

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

Solution steps

\int \frac{5}{x} + 4^{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{5}{x} d x + \int 4^{x} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int 4^{x} d x = \frac{2 ^{2 x - 1}}{ln ( 2 )}

= 5 ln ∣ x ∣ + \frac{2 ^{2 x - 1}}{ln ( 2 )}

Add a constant to the solution

= 5 ln ∣ x ∣ + \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

\int \frac{3}{x ^{2} + 81} d x

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What is the integral of (5/x+4^x) ?
The integral of (5/x+4^x) is 5ln|x|+(2^{2x-1})/(ln(2))+C