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Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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