 Hello students, let's solve the following problem of integration. We have to integrate the function x into under the root x plus 2 Let us now start the solution And let I be the integral x into under the root x plus 2 dx Now we add and subtract 2 from this So this becomes x plus 2 minus 2 Under the root x plus 2 dx. This can be again written as x plus 2 into under the root x plus 2 minus 2 into under the root x plus 2 dx We multiplied x plus 2 by under the root x plus 2 and Minus 2 with under the root x plus 2 now separating the integral. We have x plus 2 to the power 3 by 2 1 plus 1 by 2 is 3 by 2 minus 2 into integral x plus 2 to the power 1 by 2 dx and the integral of this is x plus 2 to the power 3 by 2 plus 1 upon 3 by 2 plus 1 Minus 2 into x plus 2 to the power 1 by 2 plus 1 upon 1 by 2 plus 1 Plus 3 where C is the constant of integration of both the integrals So this is again equal to x plus 2 to the power 5 by 2 upon 5 by 2 Minus 2 into x plus 2 to the power 3 by 2 upon 3 by 2 plus C Which can be again written as 2 by 5 into x plus 2 to the power 5 by 2 minus 4 by 3 Into x plus 2 to the power 3 by 2 plus C Hence the integral of the given function is 2 by 5 into x plus 2 to the power 5 by 2 minus 4 by 3 into x plus 2 to the power 3 by 2 plus C So this completes the question. Bye for now. Take care. Have a good day