22 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.kya hua hardcore bhai isme kya samjh ni aara
g(x) problem kar rha
ruk dekhta hu
i tried opening it up and applying byparts
mhm
didnt really give much
ek cheez try kr skta hai
@hardcoreisdead
integral hata de
diffrentiate mar dono side
equan banega kuch g or g' me
mtlb kuch relation aajyega
waha se ban jayega swal
g'(x)= d/dx (g(x))
ajeeb si eqn aa rhi
are nhi
left wla integral khul jayega pura
han han
right m jo g/ln wla hai
usme wo laga na division wla rule
denominator cancle ho jayega dono side
5y-5 = lnx ( y'x -y-xy) where y=g(x)
ek hi jagah khatam hoga
and rhs ka remaining divide ho jayega
solve kr theek se g(x)(1+x)=g'(x)x
aisa kuch aayega
ek br dekhle wrna fir subha likh k bhejta hu
yhi aa rha hai
cant solve further
@Real potato i have been given g(1)=e
from this i can find g'(1)
and then ek do baar aur differentiate karke g''(1) and g'''(1)
taaki pattern mil jaye
ek br subha dekhta hu yr haina
alrr
e=1 aa gya 🤡
lol
Hint: Assume the integral to be of the form e^(g(x)).f(x)
From the last term we see f(x)=1/lnx⁵ works
Thus the (1+1/x) must be derivative of g(x)
So g(x) (from the above messages, not the one in question) turns out to be x+lnx
So g(x)/(lnx)⁵ is xe^x/(ln(x))⁵
So g(x) is xe^x
Yo, did this get cleared?
After this its easy to prove nth derivative of g(x) at x=1 is (n+1)e
yet to try...
so i have to start by lnx = t => x=e^t and then apply this
+solved @SirLancelotDuLac
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