 Hello and welcome to the session. Let us discuss the following question. It says integrate the following function The given function is x upon under the root x plus 4 where x is greater than 0 Let us now proceed on with the solution and let I be the integral x upon under the root x plus 4 This can be being written as x into x plus 4 to the power minus 1 by 2 d x Now to simplify this integral we add and subtract 4 So it becomes x plus 4 minus 4 x plus 4 to the power minus 1 by 2 d x Again this integral becomes x plus 4 Into x plus 4 to the power minus 1 by 2 minus 4 into x plus 4 to the power minus 1 by 2 d x We multiplied x plus 4 with x plus 4 to the power minus 1 by 2 and minus 4 with x plus 4 to the power minus 1 by 2 Now separating the integrals x plus 4 to the power 1 minus 1 by 2 is 1 by 2 It is integral x plus 4 to the power 1 by 2 minus 4 into integral x plus 4 to the power minus 1 by 2 d x Now integral of this function is x plus 4 to the power 1 by 2 plus 1 upon 1 by 2 plus 1 minus 4 into x plus 4 to the power minus 1 by 2 plus 1 upon minus 1 by 2 plus 1 plus see where see is the constant of integration of both the integrals Now this becomes x plus 4 to the power 3 by 2 upon 3 by 2 minus 4 into x plus 4 to the power 1 by 2 upon 1 by 2 plus see and Here we have applied the formula of the integral of a x plus b whole to the power n Which is given by a x plus b whole to the power n plus 1 upon n plus 1 into a Where a is the coefficient of x and here the coefficient of x is 1 now this becomes 2 by 3 into x plus 4 to the power 3 by 2 minus 8 into x plus 4 to the power 1 by 2 Plus see again. This is equal to 2 by 3 into x plus 4 to the power 3 by 2 minus 8 can be written as 2 by 3 into 12 Into x plus 4 to the power 1 by 2 Plus see now taking x plus 4 to the power 1 by 2 common and also taking 2 by 3 common we have x plus 4 minus 12 As we take x plus 4 to the power 1 by 2 common from here. We are left with x plus 4 here and Here we are left with 12 plus see This is equal to 2 by 3 Into x plus 4 to the power 1 by 2 into x minus 8 plus see Hence the integral of the given function is 2 by 3 into x plus 4 to the power 1 by 2 into x minus 8 plus see So this completes the question and the session right for now take care. Have a good day