 Hi, welcome to our session. Let us discuss the following question. The question says evaluate integral of 2x by 1 plus x squared into 3 plus x squared with respect to x. Let us now begin with the solution. Here in this question, we have to evaluate integral of 2x divided by 1 plus x squared into 3 plus x squared with respect to x. Now we will put x squared as t differentiating both sides with respect to x. We get dt by dx equals to 2x. Now this implies dt is equal to 2x into dx. Now by substituting dt in place of 2x dx and t in place of x squared, we get integral of 1 by 1 plus t into 3 plus t with respect to t. Now we will solve this integral by using partial fractions. t plus t is equal to a by 1 plus t plus b by 3 plus t. Now this implies b into 1 plus t divided by 1 is equal to b into 1 is equal to minus 2b. b is equal to minus 1 by, we get 1 equals to a into 3 minus 1 plus b into 1 minus 1. 1 is equal to a into 2 plus b into 0 and this is equal to 1 by, take care.