What is the integral of 3/(1+9x^2)+ln(2)*2^x ?

The integral of 3/(1+9x^2)+ln(2)*2^x is arctan(3x)+2^x+C

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integral of 3/(1+9x^2)+ln(2)*2^x

\int \frac{3}{1 + 9 x ^{2}} + ln (2) \cdot 2^{x} d x

arctan (3 x) + 2^{x} + C

Solution steps

\int \frac{3}{1 + 9 x ^{2}} + ln (2) \cdot 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 \frac{3}{1 + 9 x ^{2}} d x + \int ln (2) \cdot 2^{x} d x

\int \frac{3}{1 + 9 x ^{2}} d x = arctan (3 x)

\int ln (2) \cdot 2^{x} d x = 2^{x}

= arctan (3 x) + 2^{x}

Add a constant to the solution

= arctan (3 x) + 2^{x} + C

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What is the integral of 3/(1+9x^2)+ln(2)*2^x ?
The integral of 3/(1+9x^2)+ln(2)*2^x is arctan(3x)+2^x+C