- #1
tweety1234
- 112
- 0
Homework Statement
[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