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Integral Calculus

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Joined:	6 Jan 2009
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6 Jan 2009 22:55:33 IST

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integration of {(root of cot x) - (root of tan x)} / (1+3sin2x)

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integration of {(root of cot x) - (root of tan x)} / (1+3sin2x)

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kabi

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Joined: 11 Jan 2009

Posts: 575

11 Jan 2009 23:43:12 IST

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Hello
sorry buddy as I m not going to explain it fully.
write tan(x) and cot(x) in sinx and cosx.
also sin(2x)=2sin(x)cos(x)
after doing this ur question would have cos^2(x)-sin^2(x) in numerator and sqrt(cos(x)sin(x)) * (1+6sin(x)cos(x) )in denominator.
just put sinxcosx =t^2
ur question will become 2dt/(1+3t^2)
which u can do easily.

Mirka

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Joined: 13 Aug 2008

Posts: 1313

12 Jan 2009 18:38:16 IST

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My Method

Let f(x) =

Now write sin2x in terms of sinx + cos x

that is, sin 2x = ( sinx + cosx )² - 1

So, f(x) =

Now, your integral,

I =

for this, substitute sinx + cosx = t,

u get numerator as dt

sooo...

I becomes =

substitute t² - 1 = z²,

u get

I =

this is the tan^-1 form

i think u can do it now...

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