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anilorap
 4 years ago
i want to confirm the answer of... integrate lnx/x dx
anilorap
 4 years ago
i want to confirm the answer of... integrate lnx/x dx

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anilorap
 4 years ago
Best ResponseYou've already chosen the best response.1my answer is ln lxl +c

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

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

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

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1sometimes its not always that easy though

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

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1it 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

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

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

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

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

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1tanx=sinx/cosx agree?

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

anilorap
 4 years ago
Best ResponseYou've already chosen the best response.1with the negative sign of the sin

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

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

anilorap
 4 years ago
Best ResponseYou've already chosen the best response.1then u have integral of du/u

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1negative or positive?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1yes and now integrate

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

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

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

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

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

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

anilorap
 4 years ago
Best ResponseYou've already chosen the best response.11/2 integral of du/u =1/2 lnlul+c =1/2 ln/x^2+2xl+c

myininaya
 4 years ago
Best 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?

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

anilorap
 4 years ago
Best ResponseYou've already chosen the best response.1ohh... sorry.. yes yes

myininaya
 4 years ago
Best 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?

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

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

anilorap
 4 years ago
Best ResponseYou've already chosen the best response.1yess... how can i laugh??

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

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

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

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

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

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

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1np 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
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