What is the integral of (4sec(x)tan(x)+3sec^2(x)) ?

The integral of (4sec(x)tan(x)+3sec^2(x)) is 4sec(x)+3tan(x)+C

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integral of (4sec(x)tan(x)+3sec^2(x))

\int (4 sec (x) tan (x) + 3 sec^{2} (x)) d x

4 sec (x) + 3 tan (x) + C

Solution steps

\int 4 sec (x) tan (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 4 sec (x) tan (x) d x + \int 3 sec^{2} (x) d x

\int 4 sec (x) tan (x) d x = 4 sec (x)

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

= 4 sec (x) + 3 tan (x)

Add a constant to the solution

= 4 sec (x) + 3 tan (x) + C

\frac{\partial}{\partial x} (- y^{2})

\int u^{- 3} \frac{1}{2} d u

\frac{d y}{d x} = x e^{- x}

\int_{0}^{7} \frac{5}{3} x d x

- \frac{1}{s ^{2} + ( 5 ) ^{2}}

What is the integral of (4sec(x)tan(x)+3sec^2(x)) ?
The integral of (4sec(x)tan(x)+3sec^2(x)) is 4sec(x)+3tan(x)+C