anonymous
  • anonymous
integrate dx/9+4x^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Seems like you want a trig substitution here. Something like let \(2x = 3tan(\theta)\)
anonymous
  • anonymous
polpak continue
anonymous
  • anonymous
Well, what do you end up with using that substitution?

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anonymous
  • anonymous
\[ dx=3/2\sec ^{2}x thetad \theta\]
anonymous
  • anonymous
Yeah, though you have a stray x in there I'm assuming is a typo.
anonymous
  • anonymous
So now convert your integral into the new form with respect to theta
anonymous
  • anonymous
please help idk
anonymous
  • anonymous
Well, you have \[\int \frac{1}{9+4x^2}dx\] Since 2x = 3tan\(\theta\) What does that denominator become?
anonymous
  • anonymous
\[9\sec ^{2}\theta\]
anonymous
  • anonymous
\(9 + 9tan^2\theta\)
anonymous
  • anonymous
Which yes, then becomes \(9sec^2\theta\)
anonymous
  • anonymous
Ok, now you said dx = (3/2)\(sec^2\theta\ d\theta\)
anonymous
  • anonymous
So we have \[\frac{3}{2}\int\frac{sec^2\theta}{9sec^2\theta}d\theta\]
anonymous
  • anonymous
And I think you can take it from there.
anonymous
  • anonymous
yea i got it thx.............
anonymous
  • anonymous
polpak pls solve\[\int\limits \tan ^{3}x\]
anonymous
  • anonymous
polpak i need ur help
anonymous
  • anonymous
Hrm.. I don't recall the strategy for powers of tan I'm afraid. I'll see if I can re-derive it.
anonymous
  • anonymous
ok
anonymous
  • anonymous
integration by parts
anonymous
  • anonymous
chaguanas i know it but solve it
anonymous
  • anonymous
¬_¬ \[\int \tan^3x = \int \tan x \ (\sec^2-1) = \int \tan x\ \sec^2x - \int \tan x \]
anonymous
  • anonymous
INewton pls continues
anonymous
  • anonymous
For the first one, you could use a substitution of note it is of the form \[f\ '(x) \cdot f \ (x) \] and try by recognition. \[ \int -\tan x = \int \frac{-\sin x}{\cos x}\] Which is of the form \[\frac{f \ '(x)}{f\ (x)} \] (think ln )
anonymous
  • anonymous
INewton pls solve \[\int\limits \sqrt{9-4x ^{2}}/x\]
anonymous
  • anonymous
Same type deal as the other trig sub you had before except instead of tan you let 2x = \(3 sec\theta\)
anonymous
  • anonymous
Lets see if you can do it yourself this time.

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