Again this question. We have to solve integration to X into the bracket Access where? Minus one DX. OK, so as part of the question, we have to solve it first of all by using substitution method and then without substitution. Okay, so first, with substitution, you'll substitute U equals two X squared minus one, and it will give us the week was 22 x dx. Okay. And now integration. This excess square management will be you. And these two x dx will be our d You okay, So the integration of you do you will be you square by two plus C or we can say u is X squared minus one. Then it will be X squared minus one Holy Squire by two plus c So this is the answer by using substitution method and now, without substitution, we will. It is two x and into the bracket X squared minus one DX. So we just multiply these two x and two x squared minus one. So it will be two x cube. Okay, two X cubed minus two x and D x. Okay. And by the integration, it will be two x rays to the power four divided by four minus two x squared by two plus c. Okay. Or we can say it will be X raised to the power four divided by two minus X squared plus c. Okay, so this is the answer by without substitution. Okay. And now we will check. Both of these answers are same or not, or equal or not. Okay, so left hand side, the first answer that is X squared minus one will square divided by two plus C and the right hand side X raised to the power four divided by two minus X squared, plus c. Okay, Now we will check if these answers are same or not. So we have taken question mark in between them. So first of all, we will multiply both of these side by two. And it will be X squared minus one Holy square. Okay. And plus, it will be to see that can be written again. See? Okay. And it will be expressed to the power four and minus two x Esquire. Okay. Plus, to see that can be again. See? And now we will expand the left hand side. Okay, We will. In the left hand side we will expand the square and it will be expressed to the power four. Okay. Plus one minus to a B. And it will be minus two X square plus C and question mark and access to the power four minus two X squared plus C. Okay. Here one is constant at sea is also constant. So we will miss them. Okay. And it will be expressed to the about four minus two x squared plus C and right inside access to the power four minus two x squared plus c And we see that the both sides are equal. So we make them equal and we can can grow you can You can do the integration by any method. And the answer will always be same. Thank you.