What is the integral of (3e^x+5sec^2(x)) ?

The integral of (3e^x+5sec^2(x)) is 3e^x+5tan(x)+C

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integral of (3e^x+5sec^2(x))

\int (3 e^{x} + 5 sec^{2} (x)) d x

3 e^{x} + 5 tan (x) + C

Solution steps

\int 3 e^{x} + 5 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 5 sec^{2} (x) d x

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

\int 5 sec^{2} (x) d x = 5 tan (x)

= 3 e^{x} + 5 tan (x)

Add a constant to the solution

= 3 e^{x} + 5 tan (x) + C

\frac{\partial}{\partial y} (\frac{2 y}{x + z})

\frac{d}{d x} (8 (x^{3} - x)^{4})

f (x) = 1.58 e^{- 0.213 x}

f (x) = \frac{4 x}{e ^{x}}

35 x ln (20 x)

What is the integral of (3e^x+5sec^2(x)) ?
The integral of (3e^x+5sec^2(x)) is 3e^x+5tan(x)+C