What is the integral of 7e^x+2sec^2(x) ?

The integral of 7e^x+2sec^2(x) is 7e^x+2tan(x)+C

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integral of 7e^x+2sec^2(x)

\int 7 e^{x} + 2 sec^{2} (x) d x

7 e^{x} + 2 tan (x) + C

Solution steps

\int 7 e^{x} + 2 sec^{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 7 e^{x} d x + \int 2 sec^{2} (x) d x

\int 7 e^{x} d x = 7 e^{x}

\int 2 sec^{2} (x) d x = 2 tan (x)

= 7 e^{x} + 2 tan (x)

Add a constant to the solution

= 7 e^{x} + 2 tan (x) + C

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What is the integral of 7e^x+2sec^2(x) ?
The integral of 7e^x+2sec^2(x) is 7e^x+2tan(x)+C