(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] \int \frac{3x}{2x+3} [/tex]

[tex] u = 2x +3 [/tex]

[tex] x = \frac{1}{2}(u-3} )[/tex]

[tex] dx = \frac{1}{2} du [/tex]

so now the integral should be,

[tex] \int \frac{ \frac{3u-9}{2}}{u} \times \frac{1}{2} du [/tex]

= [tex] \frac{1}{2} \int \frac{3u-9}{2} \times \frac{1}{u} du [/tex]

[tex] \frac{1}{2} \int \frac{3u-9}{2u} du [/tex]

[tex] \frac{1}{2} \int \frac{3u}{2u} - \frac{9}{2u} [/tex]

[tex] \frac{1}{2} \int \frac{3}{2} - \frac{9}{2u} [/tex]

= [tex] \frac{1}{2} [ \frac{3}{2}u - \frac{9}{2} ln(2u)] [/tex]

so final answer, after simplifying is ; [tex] \frac{3}{2}x +\frac{9}{4} - \frac{9}{4}ln(4x+6) +c [/tex]

but my book says the correct answer is [tex] \frac{3}{2}x - \frac{9}{4}ln(2x+3) +c [/tex]

So if anyone can tell me where I have gone wrong, I would really appreciate it.

thanks

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# Homework Help: Integration by substitution,

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