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Question

2x+3(2x+1)(13x)dx=

A
25log|2x+1|1115log|13x|+c
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B
25log|2x+1|1115log|1+3x|+c
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C
23log|2x1|+1115log|13x|+c
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D
25log|2x+1|215log|1+3x|+c
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Solution

The correct option is A 25log|2x+1|1115log|13x|+c
We can express the numerator as,
2x+3=A(2x+1)+B(13x)
Comparing the corresponding coefficients,
A = 115 and B=45
Thus,
2x+3(2x+1)(13x)dx=A(2x+1)dx+B(13x)(2x+1)(13x)dx
=A13xdx+B2x+1dx
=1115×ln(13x)+25×ln(2x+1)+c
Hence, option 'A' is correct.

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