khanvict
Newbie level 2
1) integral [e^(arctan x) / (1+x^2)]dx
i know proof: arctan = 1/(1+x^2)
2) integral [4dt / (t(5+(ln t)^2)]
i know proof: d/dx arcsec = 1 / (x*sqrt(x^2-1))
i am stuck on both of these so any help is appreciated. thanks in advance!
Added after 4 hours 12 minutes:
here is what i did with the 2nd:
integral 4 dt / (t [ 5 + (ln 2)^2 ])
rewritten:
integral [ 4 / t * ( 1 / (5 + (ln t)^2) ) ]
and again:
integral [ (4t^-1) * ( 1 / (5 + (ln t)^2) ) ]
trying to get the 2nd half in proof form of: arctan = (du / 1 + u^2)
& noting that proof: x^p = ln x + c if p = -1
i ended up with:
(1/5)t * [(4 ln t) * arctan(ln t)] + c
i have no idea if that's correct but i only have 2 hours left so i have to go with it.
anyone reading this know how to do the 1st by any chance?
i know proof: arctan = 1/(1+x^2)
2) integral [4dt / (t(5+(ln t)^2)]
i know proof: d/dx arcsec = 1 / (x*sqrt(x^2-1))
i am stuck on both of these so any help is appreciated. thanks in advance!
Added after 4 hours 12 minutes:
here is what i did with the 2nd:
integral 4 dt / (t [ 5 + (ln 2)^2 ])
rewritten:
integral [ 4 / t * ( 1 / (5 + (ln t)^2) ) ]
and again:
integral [ (4t^-1) * ( 1 / (5 + (ln t)^2) ) ]
trying to get the 2nd half in proof form of: arctan = (du / 1 + u^2)
& noting that proof: x^p = ln x + c if p = -1
i ended up with:
(1/5)t * [(4 ln t) * arctan(ln t)] + c
i have no idea if that's correct but i only have 2 hours left so i have to go with it.
anyone reading this know how to do the 1st by any chance?
