What is the integral of 2/(1+4x^2)+ln(8)*8^x ?

The integral of 2/(1+4x^2)+ln(8)*8^x is arctan(2x)+8^x+C

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integral of 2/(1+4x^2)+ln(8)*8^x

\int \frac{2}{1 + 4 x ^{2}} + ln (8) \cdot 8^{x} d x

arctan (2 x) + 8^{x} + C

Solution steps

\int \frac{2}{1 + 4 x ^{2}} + ln (8) \cdot 8^{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{2}{1 + 4 x ^{2}} d x + \int ln (8) \cdot 8^{x} d x

\int \frac{2}{1 + 4 x ^{2}} d x = arctan (2 x)

\int ln (8) \cdot 8^{x} d x = 8^{x}

= arctan (2 x) + 8^{x}

Add a constant to the solution

= arctan (2 x) + 8^{x} + C

What is the integral of 2/(1+4x^2)+ln(8)*8^x ?
The integral of 2/(1+4x^2)+ln(8)*8^x is arctan(2x)+8^x+C