 Hi and welcome to the session. Let's work out the following question. The question says evaluate integral x dx divided by x plus 2 into 3 minus 2x. Hi and welcome to the session. Let's work out the following question. The question says evaluate integral x dx divided by x plus 2 into 3 minus 2x. Let us start with the solution to this question. First of all, let x divided by x plus 2 into 3 minus 2x. We written as a divided by x plus 2 plus b divided by 3 minus 2x. This implies x divided by x plus 2 into 3 minus 2x is equal to a into 3 minus 2x plus b into x plus 2 divided by x plus 2 into 3 minus 2x. We see that denominators get cancelled from both the side because they are just the same. This implies that x is equal to a into 3 minus 2x plus b into x plus 2. Now, first of all we put x to be equal to minus 2 then minus 2 is equal to a into 3 plus 4. And this becomes 0. This implies a is equal to minus 2 by 7. Now, we put x to be equal to 3 by 2 then 3 by 2 is equal to a into 0 plus b into 3 by 2 plus 2. This implies that b is equal to 3 by 2 multiplied by 2 by 7 that is equal to 3 by 7. So, integral i can now be written as integral x dx divided by x plus 2 into 3 minus 2x is same as integral minus 2 divided by 7 into x plus 2 plus 3 by 7 into 3 minus 2x dx. This is equal to minus 2 by 7 and dx by x by 2 this will integral give us log mod x plus 2 plus. Now, we see that this can be written as minus 1 by 2 into 3 by 7 into integral minus 2 dx by 3 minus 2x. Here we have plus 3 here we have minus 3 by 14. This gives us log mod 3 minus 2x minus 2c that is equal to minus 2 by 7 log mod x plus 2 minus 3 by 14. Log mod 3 minus 2x plus the constant c. So, this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.