00:01
So here the problem sees use the specified substitution to find or evaluate the integral and it is also said use c for the constant of integration.
00:14
So integration root over x minus 7 upon x plus 2 is given to us.
00:22
Right.
00:23
And we are also given u equals to root over x minus 7.
00:28
So these are given conditions for us and we will solve this.
00:34
We will just integrate it after substituting.
00:41
Right.
00:42
So now we can say here it is given u equals to root over x minus 7.
00:50
Also x equals to u squared plus 7.
00:54
Can we write this equation in this way? yes.
00:57
So we will just differentiate this equation so we will finally get this is n x n minus 1 so this is just the value like this we get this equation like this so this is 1 by 2 root over x minus 7 so it is equal to 1 upon 2 u so this is given by what d x d x equals to 2 u d u right now, now we can write here, let us say your integration will be represented, let us suppose it as i.
01:41
So integration will be what? it will be simply, this is root over x minus 7 is you, right, in terms of you.
01:51
And x plus 2 is there.
01:53
So, x plus 2, x plus 2 is replaced by, this is actually x is replaced by, this is actually x is replaced by u square plus 7 right and this is plus 2 remember this is plus 2 so now d x is replaced by what 2 u d u all right so this is how we will solve this this will give us i equals to integration u by you can say this is 2 u square all right so this will be u square plus 9...