What is the integral of 5/(1+25x^2)+ln(7)*7^x ?

The integral of 5/(1+25x^2)+ln(7)*7^x is arctan(5x)+7^x+C

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integral of 5/(1+25x^2)+ln(7)*7^x

\int \frac{5}{1 + 25 x ^{2}} + ln (7) \cdot 7^{x} d x

arctan (5 x) + 7^{x} + C

Solution steps

\int \frac{5}{1 + 25 x ^{2}} + ln (7) \cdot 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{5}{1 + 25 x ^{2}} d x + \int ln (7) \cdot 7^{x} d x

\int \frac{5}{1 + 25 x ^{2}} d x = arctan (5 x)

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

= arctan (5 x) + 7^{x}

Add a constant to the solution

= arctan (5 x) + 7^{x} + C

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What is the integral of 5/(1+25x^2)+ln(7)*7^x ?
The integral of 5/(1+25x^2)+ln(7)*7^x is arctan(5x)+7^x+C