DHASHNI
can any one help me!!!!!
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DHASHNI
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|dw:1327218851048:dw|
DHASHNI
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its calculus
wasiqss
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is it t+1 in the bracket
DHASHNI
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no its inside log
Jemurray3
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Is that
\[ \int_1^x \frac{B\cdot \log(1+t)}{1+t^2} dt \]
DHASHNI
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\[\int\limits_{0}^{1} \frac{8\ln(1+t)}{1+t^2} \]
DHASHNI
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its this ^
Jemurray3
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This looks like a pretty nasty integral, what class is this for? :)
Jemurray3
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My first thought would be integration by parts, actually.
wasiqss
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ok now i got it
DHASHNI
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@jem: i am a high school student :P
DHASHNI
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@was : can u help!!!!
DHASHNI
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help
wasiqss
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ok i wud go in this way by integration by parts
take 8 out
now u left with (\[8\int\limits_{x}^{1}(\ln(1+t)/(1+t^2)\]
now take 1/(1+t^2) as part to integrate , and derivative ln (1+t)
Aron_West
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\[\pi \log(2)\]
Aron_West
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~~2.17759
wasiqss
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integral of 1/(1+t^2) is tanx
Jemurray3
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arctan^
wasiqss
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yehh jemurray typo
DHASHNI
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@aron: hw did you got the ans ? can you show the steps ?
@was:then?
wasiqss
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dhash i have simplified enuf lol
DHASHNI
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i got '0=0' thats why i am asking you
wasiqss
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use integration by parts, i have told u what to integrate and what to differentiate ,
DHASHNI
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i didnot get the ans in that way
Jemurray3
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You've neglected to mention the integral
\[ \int_0^1 \frac{\tan^{-1}(x)}{1+x} dx \]
which is pretty damn complicated, I would say.
Aron_West
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4 i (-Li_2((1/2-i/2) (t+1))+Li_2((1/2+i/2) (t+1))+log(t+1) (log((-1/2-i/2) (t+i))-log(1-(1/2-i/2) (t+1))))+constant
DHASHNI
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yep jem is right
Aron_West
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Now, just plug in the limits.
Jemurray3
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With respect Aron, we all know how to use wolfram alpha.
wasiqss
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haha jem
wasiqss
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jem bt what else cud b easier way other than by parts to teach a high scool student
Jemurray3
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you're missing my point, integration by parts still requires you to solve that integral I wrote, which is kinda rough.
wasiqss
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i know jemm im tryin to simplify it
Aron_West
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Try x = tan y
wasiqss
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yeah got it place t =arctany
then its simple
DHASHNI
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cool thanks that works