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integrate the following integral ∫ 2x / (2x + 1)^2 dx

 
integrate the following integral
∫ 2x / (2x + 1)^2 dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{2x}{(2x+1)^2}dx
I = \int \frac{2x+1-1}{(2x+1)^2}dx
I = \int [\frac{1}{2x+1}-\frac{1}{(2x+1)^2}]dx
I = \int \frac{1}{2x+1}dx-\int \frac{1}{(2x+1)^2}dx
I = \frac{log(2x+1)}{2}-\int \frac{1}{(2x+1)^2}dx
I = \frac{log(2x+1)}{2}+ \frac{1}{2(2x+1)}+c

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