Question

integration of 4x+3/2x+1 .dx​

Answer 1

Answer:

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Answer 2

Answer:

Integration of 4x+3/2x+1 .dx is: ​2x +   $\frac{1}{2}$ ㏒|2x+1| + c

Step-by-step explanation:

• Integration: Integration is a process where the parts are sums up to get whole . This is a reverse process of derivative (where a whole function splits into some parts).
• Integration Constant: At the time of integrating the sub parts a constant is added to the whole, which is called as integration constant.

• Step-1: The function can be written in the following form-

                  $\frac{4x+3}{2x+1}$ = $\frac{4x+2+1}{2x+1}$

                           =$\frac{2(2x+1)+1}{2x+1}$ = 2 + $\frac{1}{2x+1}$

• Step-2:  By integrating the function,

            ∫ $\frac{4x+3}{2x+1}$ dx = ∫(2 + $\frac{1}{2x+1}$) dx + c   [ c = integration constant]

                                    = 2∫dx + ∫ $\frac{1}{2x+1}$ dx + c

                                    = 2x + $\frac{1}{2}$ ∫ $\frac{1}{2x+1}$ d(2x + 1) + c

                                    = 2x +   $\frac{1}{2}$ ㏒|2x+1| + c

         ∴Integration of 4x+3/2x+1 .dx is: ​2x +   $\frac{1}{2}$ ㏒|2x+1| + c