What is the integral of 3/x+e^{2x}-7^x ?

The integral of 3/x+e^{2x}-7^x is 3ln|x|+1/2 e^{2x}-(7^x)/(ln(7))+C

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integral of 3/x+e^{2x}-7^x

\int \frac{3}{x} + e^{2 x} - 7^{x} d x

3 ln ∣ x ∣ + \frac{1}{2} e^{2 x} - \frac{7 ^{x}}{ln ( 7 )} + C

Solution steps

\int \frac{3}{x} + e^{2 x} - 7^{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{3}{x} d x + \int e^{2 x} d x - \int 7^{x} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

\int 7^{x} d x = \frac{7 ^{x}}{ln ( 7 )}

= 3 ln ∣ x ∣ + \frac{1}{2} e^{2 x} - \frac{7 ^{x}}{ln ( 7 )}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{1}{2} e^{2 x} - \frac{7 ^{x}}{ln ( 7 )} + C

What is the integral of 3/x+e^{2x}-7^x ?
The integral of 3/x+e^{2x}-7^x is 3ln|x|+1/2 e^{2x}-(7^x)/(ln(7))+C