Integrate (3x+4)/(5x+2) with respect to x
2006-12-31 05:17:59 · 7 answers · asked by ndavos 2 in Science & Mathematics ➔ Mathematics
Integrate (3x+4)/(5x+2) with respect to x.
First break up the fraction, then integrate. Use division and you will find:
(3x+4)/(5x+2) = 3/5 + (14/5)/(5x + 2) = (1/5)[3 + 14/(5x + 2)]
Now integrate.
∫(3x+4)/(5x+2) dx = ∫{(1/5)[3 + 14/(5x + 2)]} dx
=(1/5){3x + (14/5)ln|5x + 2|} + C
= (3/5)x + (14/25)ln|5x + 2| + C
2006-12-31 08:38:40 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋
First seperate the equation into two parts.
[3x/(5x+2)] + [4/(5x+2)]
Now you can integrate them seperately. You can seperate the first equation into (5/3) + 2/(5x+2). You can do a u substitution for 5x+2. So you get the integral of (5/3)dx + 2/(5u) du + 4/(5u) du. Integrate that and substitue u back in and you will get your answer and don't forget to put the +c so you have all possible answers.
2006-12-31 05:38:19 · answer #2 · answered by shmousy636 3 · 0⤊ 0⤋
Use mental substitution:
(3x+4)/(5x+2)
= [3(5x+2)/5 - 6/5 + 4]/(5x+2)
= 3/5 + (14/5)/(5x+2)
∫(3x+4)/(5x+2) dx
= ∫(3/5 dx + ∫(14/25)/(5x+2) d(5x+2)
= 3x/5 + (14/25) ln|5x+2| + c (mental substitution: u = 5x+2)
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Mental substitution should be widely used in integration because it can help you to find the right direction to do substitution. In addition, it is simpler if you get familiar with it.
2006-12-31 05:42:13 · answer #3 · answered by sahsjing 7 · 1⤊ 1⤋
Shashing is on the right track with these "easier" integrals: with practice it becomes easier to "see" the answer. I would add: check with tehcnology:
> int((3*x+4)/(5*x+2) ,x);
14
3/5 x + -- ln(25 x + 10)
25
Output from Maple is messy but it checks with other answer (except for an integration constant)
2006-12-31 06:46:47 · answer #4 · answered by a_math_guy 5 · 0⤊ 0⤋
write as (3x+4)(5x+2)^ -1 then use the product rule.
2006-12-31 05:24:37 · answer #5 · answered by christopher_az 2 · 0⤊ 1⤋
3/5[5x+2]/5x+2 +14/5(5x+2)
now it is in standardform.integrate
2006-12-31 05:30:22 · answer #6 · answered by raj 7 · 1⤊ 1⤋
3x+5x =8x follow so far ?....like terms go together, they just can't get enuff of each other from what i remember....4+2=6 OK...so it should be 8x6 ...i think.... the answer is 48...or just 8x6 i 4get if you can't do any thing with unlike terms or some thing like that ...man do your own work, my head hurts now...see if i ever help you again ^_^
2006-12-31 05:24:42 · answer #7 · answered by Anonymous · 0⤊ 2⤋