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anilorapBest ResponseYou've already chosen the best response.1
my answer is ln lxl +c
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
let u=lnx du=dx/x \[\int\limits_{}^{}u du=\frac{u^2}{2}+C=\frac{(lnx)^2}{2}+C\] we can even check this: \[(\frac{(lnx)^2}{2}+C)'=2*\frac{lnx}{2}*\frac{1}{x}+0=\frac{lnx}{x}\]
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
q. how do i know what to choose?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
i was looking for \[\int\limits_{}^{}f(x)*f'(x)dx\]
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
sometimes its not always that easy though
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
someone said it is like an art and i agree
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
it is not always easy to know what substititon to make but since it was in the form of above it was easy let u=f(x) du=f'(x) dx
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[\int\limits_{}^{}\frac{lnx}{x}dx=\int\limits_{}^{}lnx*\frac{1}{x} dx\]
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
so it was easy for me to notice pretty fast that (lnx)'=1/x so thats why i let u=lnx
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
so how can i integrate tanx dx..... even though i know thats it is equal to lnlcosxl+c
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[\int\limits_{}^{}\frac{sinx}{cosx} dx\] right?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
tanx=sinx/cosx agree?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
now what do you think the substitution will be?
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
with the negative sign of the sin
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
du=sinx dx (i like not to forget about this dx part)
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
so show me what that gives us don't integrate yet
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
then u have integral of du/u
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
negative or positive?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
yes and now integrate
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
so my result will be ln/u/+c
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
so whats this \[\int\limits_{}^{}tanx dx\] equal to?
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
becuase the negative sign will change to postive once u take the derivative of cosx
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
you want to try one i made up? its not hard
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[\int\limits_{}^{}\frac{x+1}{x^2+2x}dx\]
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
u=x^2 + 2x du=2x+2 dx =2(x+1) dx so, 1/2du=x+1 dx
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
1/2 integral of du/u =1/2 lnlul+c =1/2 ln/x^2+2xl+c
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[\int\limits_{}^{}\frac{f'(x)}{f(x)}dx\] so when we have this what will out answer be in the form of?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
look at the one you just did didn't we have f'/f dx?
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
ohh... sorry.. yes yes
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
\[\int\limits_{}^{}[f(x)]^n*f'(x)dx\] \[n \neq 1\] what about this? what will our answer be?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
i will give you a hint let u=f(x) so du=f'(x) dx
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
where are you from? you say jajaja alot lol
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
yess... how can i laugh??
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
its fine the way you type your laughter no worries i like it
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
so this all makes a little more sense?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
im asking do you get the integral stuff better?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
good :) im fixing to go to sleep goodnight
 2 years ago

anilorapBest ResponseYou've already chosen the best response.1
for me is mornig.. but good nigth,,,
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
good morning* i didn't sleep all night lol
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
np if you want to try another this is a good one \[\int\limits_{}^{}x*\sqrt{x+1} dx\] the answer is given above in one of the other threads if you want to check yourself
 2 years ago
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