1 divided by (9x²+12x+4)
how do you integrate that?
thanx
2006-09-17 02:23:26 · 6 answers · asked by vanille 1 in Science & Mathematics ➔ Mathematics
wel vanille;
f(x) = 1/ (9x²+12x+4)
∫1/ (9x²+12x+4) = Log (4 + 21*x) / 21 + c
Its our correct answer.
Good Luck.
2006-09-17 02:51:23 · answer #1 · answered by sweetie 5 · 0⤊ 1⤋
First recognize that (9x²+12x+4) = (3x + 2)²
Now let u = 3x + 2 and du = 3dx
The result is -1 / (9x+6)
2006-09-17 09:31:21 · answer #2 · answered by z_o_r_r_o 6 · 0⤊ 0⤋
I agree, Zorro saved the day here and he also forgot the 'C'. Shame on you, j/k. You just factor the denominator and U substitute.
If you do want to check your answers you can simply differentiate (which you'll find true here) or while at home you can use http://integrals.wolfram.com to get an answer. But remember you still need to know how to get to the answer. This is just a way of checking.
2006-09-17 11:38:54 · answer #3 · answered by Mike B 1 · 0⤊ 1⤋
9x^2+12x+4=(3x+2)^2
put 3x+2=t
3dx=dt
integral=(-2/3)/(3x+1) +C
2006-09-17 09:32:47 · answer #4 · answered by raj 7 · 0⤊ 1⤋
Zorro is the only right answer (except that the +C was forgotten). This integral will not involve logarithms!
2006-09-17 10:26:54 · answer #5 · answered by mathematician 7 · 1⤊ 1⤋
log(9x²+12x+4)
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12
2006-09-17 09:30:04 · answer #6 · answered by Keex 2 · 0⤊ 0⤋