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

x \to 1 lim (ln (2 x) + e^{x})

\frac{11}{( s - 1 ) ^{3}}

\int_{0}^{2} 8 x - \frac{1}{8} x d x

n = 0 \sum \infty 2 x^{2 n}

\int_{3}^{\infty} e^{- x} d x

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