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

The integral of (sec(2x)+tan(2x)) is 1/2 ln|tan(2x)+sec(2x)|-1/2 ln|cos(2x)|+C

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integral of (sec(2x)+tan(2x))

\int (sec (2 x) + tan (2 x)) d x

\frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣ - \frac{1}{2} ln ∣ cos (2 x) ∣ + C

Solution steps

\int sec (2 x) + tan (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 sec (2 x) d x + \int tan (2 x) d x

\int sec (2 x) d x = \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣

\int tan (2 x) d x = - \frac{1}{2} ln ∣ cos (2 x) ∣

= \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣ - \frac{1}{2} ln ∣ cos (2 x) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣ - \frac{1}{2} ln ∣ cos (2 x) ∣ + C

f (x) = \frac{2 t + 1}{t + 3}

y = 2 x^{2} + 3, (0, 3)

\int \frac{x ^{2} + 1}{1 - x ^{2}} d x

x \to \frac{5 π}{6} lim (sin (x))

\frac{d y}{d x} = (x y)^{2}, y (0) = 1

What is the integral of (sec(2x)+tan(2x)) ?
The integral of (sec(2x)+tan(2x)) is 1/2 ln|tan(2x)+sec(2x)|-1/2 ln|cos(2x)|+C