00:01
In this question, we need to find the value of integration dx upon under root x squared minus 2x minus 3.
00:14
Let's see how to solve this question.
00:16
Consider x minus 1 is equal to 2 secant u.
00:26
Therefore, by the differentiation we can write, dx is equal to 2 secant u, tangent u, d u.
00:44
Since the whole square of x minus 1 is equal to x square minus 2x plus 1, hence the given integration can be written as integration dx upon under root x minus 1 to the power 2 minus 4.
01:14
Now substitute x minus 1 is equal to 2 secant u and dx is equal to 2ccent u tangent u.
01:21
Hence, the integration becomes 2 secant u, tangent u d u upon under root 2 square securc second u minus 4 and this will be equals to integration 2 secant u d u upon 2 under root secant square u minus 1 we know that 1 plus tangent square theta is equals to secant square theta hence the value of second square theta minus 1 will be equals to tangent square theta so based on this value the above integration can be written as integration to secant u tangent u d u upon 2 tangent u.
02:44
On further solving, we can write this integration as integration secant u the integration of secant u is equal to log secant u plus tangent u.
03:10
Since we have already considered x minus 1 is equal to 2 seccent u hence the value of second will be equals to x minus 1 upon 2...