 Let's take the application of these special exegers which we just now learnt in the 6th of course. See this plus A plus A. So likewise which can be written as 1 by 3. 2 can be taken in the same way. Yeah. You can write it like this. Partial. Okay. Yeah this is going to solve your partial fraction but however it is 2x squared plus x minus 1 as 2x squared plus 2x minus x minus 1. So it will be 1 by 2x minus 1 into x plus 1. So I will just see whether my answer is coming out to be the same. Okay. So first of all 1 by 2x squared fraction in this way. Okay. Let's find A and 2 by 3 2x minus 1 minus 1 by 3 x plus 1. So apply dx. Integrate both x. So this will be 2 by 3 ln mod 2x minus 1 by 2 will go out. And this will be minus root 2 comma root 2. Please do not do that. You can take 2 out. No issues. But don't take minus. So if I have this all. Now see minus x minus 3 by 4 whole squared minus 9 by 16 minus half. What will it become? 1 by 16. Yeah. Which is 1 by 4 whole squared minus x minus 3 by 4 whole squared. If it's into the integral dx under root a squared minus x squared extension of x. So nothing to worry. You can use the same formula. In case where you have some coefficient along with x over s. For example, use the same formula. How can you take the coefficient of x? Right. coefficient of x squared. I'll be making it once. So that situation does not arise. But in case if you want to, you can always follow that as cathode as well. So this will give you 1 by root 2. And this will be sine inverse of x by x minus 3. So suppose it is 2x minus 3 by 4 will be 1 by 2 root 3 sine inverse. Whatever. Yes. Yes. S a squared. Whose answer was s is t minus plus c. C formula if you would recall. Sine square by sine square. You are too personal. By the root of s t squared. And this becomes sine square alpha. Sine minus sine alpha. S k squared minus sine alpha. So completing it backwards which is root cos x minus sine x. So sine x will become minus 2 by 3 minus 2 by 3 dt. So your answer will be auto procedure. Same thing always. 2 by 3 sine inverse 3 by 8 divided by 3.