What is the Integration of Sec2x | Integral of Sec 2x

Answer: The integration of Sec2x is equal to (1/2) ln|Sec2x+tan2x|+C. So the formula for the integral of Sec 2x is given by

$\displaystyle \int \sec 2x~dx=\dfrac{1}{2}\ln|\sec 2x +\tan 2x|$ $+C$

where C denotes an integral constant.

Note: To find the integral of sec2x, we will use the integral of secx which is as follows: $\displaystyle \int \sec x~dx=\ln|\sec x +\tan x|$ $+C$.

What is the Integration of Sec2x?

Answer:

Here we need to find $\displaystyle \int \sec 2x~dx$.

Let us put $2x=z$. So $2dx=dz \Rightarrow dx=\dfrac{dz}{2}.$

Therefore, $\displaystyle \int \sec 2x~dx$

= $\displaystyle \int \sec z~\dfrac{dz}{2}$

= $\dfrac{1}{2}\displaystyle \int \sec z~dz$

= $\dfrac{1}{2}\ln|\sec z +\tan z|+C$

= $\dfrac{1}{2}\ln|\sec 2x +\tan 2x|+C$ as z=2x.

Comparison of Results

Expression	Integral
sec(2x)	$\dfrac{1}{2}\ln|\sec 2x +\tan 2x|+C$
sec2x	tan(x)+C
sec2(2x)	$\dfrac{1}{2}$ tan(2x)+C

Also Study: Integral of sec²x

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