 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says In TL of under root of x squared minus 8x plus 7 dx is equal to a 1 over 2 into x minus 4 into under root of x squared minus 8x plus 7 plus 9 log mod of x minus 4 plus under root of x squared minus 8x plus 7 plus c. b 1 by 2 into x plus 4 into under root of x squared minus 8x plus 7 plus 9 log mod of x plus 4 plus under root of x squared minus 8x plus 7 plus c 1 by 2 into x minus 4 into under root of x squared minus 8x plus 7 minus 3 root 2 log mod of x minus 4 plus under root of x squared minus 8x plus 7 plus c. d 1 over 2 into x minus 4 into under root of x squared minus 8x plus 7 minus 9 over 2 log mod of x minus 4 plus under root of x squared minus 8x plus 7 plus c. Let us first understand one special type of standard integral which is integral of under root of x squared minus a squared dx is equal to x over 2 into under root of x squared minus a squared minus a squared upon 2 into log of mod x plus under root of x squared minus a squared plus c where c is the constant of integration. So this is the key idea behind our question. We will take the help of this key idea to solve the upper question. So let us start the solution. Now our given integral is integral of under root of x squared minus 8x plus 7 dx. Now we can rewrite our given integral as integral of under root of x squared minus 8x plus 7 plus 9 minus 9 dx. Now this is equal to integral of under root of x squared minus 8x plus 16 minus 9 dx. Now we can again write this integral as integral of under root of x minus 4 whole square minus 3 square root of x squared minus a squared dx is equal to x over 2 into under root of x squared minus a squared minus a square over 2 into log of mod x plus under root of x squared minus a squared plus c integral is equal to 1 by 2 minus a squared which is x minus 4 whole square minus 3 square minus 1 upon 2 which is 9 over 2 into log of mod root of x squared minus a square that is x minus 4 whole square minus 3 square plus c 1 over 2 into x minus x square minus 8x plus 7 minus 9 by 2 into log mod of under root of x squared minus 8x plus 7 plus c you do the question it is our option for the above question is g. The solution is clear to you and you have enjoyed the session. Bye.