amorfide
integrate
1/3x+2
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amorfide
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|dw:1350485381398:dw|
amorfide
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is this right?
amorfide
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@ParthKohli
Zarkon
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+c
amorfide
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that stupid freaking C lol
ParthKohli
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Yeah, that is and then a constant... don't forget the constant.
amorfide
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parth tell me how to integrate this one...
amorfide
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|dw:1350485522236:dw|
ParthKohli
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\[2\int{dx \over x^2 + 3}\]That's tricky stuff: trig substitution.
amorfide
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i literally cant do it :P
ParthKohli
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no no no... wait
ParthKohli
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not trig substitution
amorfide
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if it was
2/x²+1
it would be a trig function
ParthKohli
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@Zarkon Please, if you might be able to help?
Zarkon
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you can use trig sub
ParthKohli
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Got it
ParthKohli
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How?
Zarkon
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\[x=\sqrt{3}\tan(\theta)\]
amorfide
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huh explain?
ParthKohli
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Oh, yup...that makes sense.
ParthKohli
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@amorfide Trigonometric substitution! Search it on Google.
Zarkon
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if you have \[\int\frac{2}{x^2+1}dx\]
then just recall that \(\displaystyle\frac{d}{dx}\tan^{-1}(x)=\frac{1}{x^2+1}\) and therefore
\[\int\frac{2}{x^2+1}dx=2\cdot\tan^{-1}(x)+c\]
if you want \[\int\frac{2}{x^2+3}dx\] then, if you want, you can use the substitution I gave above
amorfide
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so if
2/(x²+1) = 2tan^-1(x/root1) all over root 1
2/(x²+3)
=
|dw:1350487017539:dw|
Zarkon
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+c ;)
amorfide
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LOL thank you! always forget the C... would i lose a mark for not putting +c if i do not need to figure out C?
Zarkon
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yes
amorfide
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ahh okay, thank you :D
Zarkon
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there will be a time in the future when you will find a value for C. Particularly when doing initial value differential equations