What is the integral of 4/(1+16x^2)+ln(5)*5^x ?

The integral of 4/(1+16x^2)+ln(5)*5^x is arctan(4x)+5^x+C

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integral of 4/(1+16x^2)+ln(5)*5^x

\int \frac{4}{1 + 16 x ^{2}} + ln (5) \cdot 5^{x} d x

arctan (4 x) + 5^{x} + C

Solution steps

\int \frac{4}{1 + 16 x ^{2}} + ln (5) \cdot 5^{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{4}{1 + 16 x ^{2}} d x + \int ln (5) \cdot 5^{x} d x

\int \frac{4}{1 + 16 x ^{2}} d x = arctan (4 x)

\int ln (5) \cdot 5^{x} d x = 5^{x}

= arctan (4 x) + 5^{x}

Add a constant to the solution

= arctan (4 x) + 5^{x} + C

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What is the integral of 4/(1+16x^2)+ln(5)*5^x ?
The integral of 4/(1+16x^2)+ln(5)*5^x is arctan(4x)+5^x+C