What is the integral of (7e^x+3sec^2(x)) ?

The integral of (7e^x+3sec^2(x)) is 7e^x+3tan(x)+C

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integral of (7e^x+3sec^2(x))

\int (7 e^{x} + 3 sec^{2} (x)) d x

7 e^{x} + 3 tan (x) + C

Solution steps

\int 7 e^{x} + 3 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 3 sec^{2} (x) d x

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

\int 3 sec^{2} (x) d x = 3 tan (x)

= 7 e^{x} + 3 tan (x)

Add a constant to the solution

= 7 e^{x} + 3 tan (x) + C

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What is the integral of (7e^x+3sec^2(x)) ?
The integral of (7e^x+3sec^2(x)) is 7e^x+3tan(x)+C