Friends out there.... HELP!!! Please help me with this one:

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Friends out there.... HELP!!! Please help me with this one:

Mathematics
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@ganeshie8 please help me. :) @mathmate please help me. :)
wht do u think??? @itsmeeQUENNIE i first of all used substitution and then used the ILATE rule.. and thts lengthy

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i think ...i will use the LIATHE.. and yeah.. you're right.. it's lengthy...
the suppose e^x = u so e^x dx = du dx = du/(e^x)
use these substitution
why you use first the exponential form?
i didn't get tht....wht do u mean???
why you let u = e^x, instead of letting u = cos e^-x ... it is in the rule, right? the LIATHE!
u can even apply e^x = u so cos(e^{-x}) = cos(1/u) so the integral would be \[\int\limits u^3 \cos(\frac{ 1 }{ u }) du\]
And @itsmeeQUENNIE tbh thanks for postng this creepy question..... made me recall whole chapter :)
hihih.. you're welcome. :)
btw.. i'll try to use your solution...
go on....... :) i got the the answer though ....its damn creepy :P
really? hmm.. wait.. :)
okay :) take ur time :P
@itsmeeQUENNIE u know about using ILATE ??
hey! will i use integration by part>???
yes.. i know that thing. :)
@rishavraj hey! i don't know what to do. :(
go for integration by parts :)
let v = u^3 dv = 3u^2du dw = cos (1/u) du w = ???? --> i don't know the answer. :3
hold on the integral is \[\int\limits u^3 \cos \frac{ 1 }{ u } du\] first function is u^3 and second function is cos(1/u)
yes.. then?
see \[\int\limits u~v ~~dx = u~(\int\limits~v~dx) - \int\limits ({\frac{ du }{ dx } \int\limits v~dx}) ~dx\]
u is the first function and v is the second function
in ur question u = u^3 and v = cos (1/u)
uhh.. okay... then???
now wht...just step further ...hold on i m uploading a pic...might be useful
my head is aching. waah! how to use the LIATHE again???
i think LIATHE is same as ILATE
when i was in 2nd yr college... my prof taught the LIATHE in my integral calculus subject... L - for logarithmic, I - for inverse, A - for algebraic, T - for trigonometric, H - for hyperbolic and E - for exponential...
:(
haaay. :( hopeless...
yup same except the hyperbolic one :P
@ganeshie8 hey! please teach me on this one.. pretty please???
and i went to hav dinner ...so
so apply tht ....its easy .too lengthy though
@itsmeeQUENNIE u knowing the significance of LIATHE .wht it is used for??
i don't know how to do that.. it's too complicated for me...
see u^3 is first function and cos(1/u) is second so hold on i m gonna upload a pic

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