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

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

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

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

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

Solution steps

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

\int 3 e^{x} d x = 3 e^{x}

\int 7 sec^{2} (x) d x = 7 tan (x)

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} + e ^{y}})

x \to - 2 lim (x)

\int \frac{x ^{2} + 1}{( x - 9 ) ( x - 8 ) ^{2}} d x

\frac{d}{d x} ((x^{2} + x) 3^{x})

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