anonymous
  • anonymous
i want to confirm the answer of... integrate lnx/x dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
my answer is ln lxl +c
myininaya
  • myininaya
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: \[(\frac{(lnx)^2}{2}+C)'=2*\frac{lnx}{2}*\frac{1}{x}+0=\frac{lnx}{x}\]
myininaya
  • myininaya
do you got it?

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anonymous
  • anonymous
yes
myininaya
  • myininaya
k :)
anonymous
  • anonymous
q. how do i know what to choose?
myininaya
  • myininaya
i was looking for \[\int\limits_{}^{}f(x)*f'(x)dx\]
myininaya
  • myininaya
sometimes its not always that easy though
myininaya
  • myininaya
someone said it is like an art and i agree
anonymous
  • anonymous
jajaj..ok
myininaya
  • myininaya
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
myininaya
  • myininaya
\[\int\limits_{}^{}\frac{lnx}{x}dx=\int\limits_{}^{}lnx*\frac{1}{x} dx\]
myininaya
  • myininaya
so it was easy for me to notice pretty fast that (lnx)'=1/x so thats why i let u=lnx
anonymous
  • anonymous
ok..perfect
anonymous
  • anonymous
so how can i integrate tanx dx..... even though i know thats it is equal to -lnlcosxl+c
myininaya
  • myininaya
\[\int\limits_{}^{}\frac{sinx}{cosx} dx\] right?
myininaya
  • myininaya
tanx=sinx/cosx agree?
anonymous
  • anonymous
ohhhhhhhh... ok
anonymous
  • anonymous
yes
anonymous
  • anonymous
so that du/u
myininaya
  • myininaya
now what do you think the substitution will be?
anonymous
  • anonymous
with the negative sign of the sin
anonymous
  • anonymous
u=cos
anonymous
  • anonymous
du=sin x
anonymous
  • anonymous
sorry du=-sinx
myininaya
  • myininaya
du=-sinx dx (i like not to forget about this dx part)
anonymous
  • anonymous
oh yea
myininaya
  • myininaya
so show me what that gives us don't integrate yet
anonymous
  • anonymous
then u have integral of du/u
myininaya
  • myininaya
negative or positive?
anonymous
  • anonymous
- integral of du/u
myininaya
  • myininaya
yes and now integrate
anonymous
  • anonymous
so my result will be -ln/u/+c
anonymous
  • anonymous
-ln/cosx/+c
myininaya
  • myininaya
yes :)
anonymous
  • anonymous
yeaaa thank uuuu
myininaya
  • myininaya
np
myininaya
  • myininaya
so whats this \[\int\limits_{}^{}-tanx dx\] equal to?
anonymous
  • anonymous
ln/cosx/+c
anonymous
  • anonymous
becuase the negative sign will change to postive once u take the derivative of cosx
anonymous
  • anonymous
why u pic u =sinx?
myininaya
  • myininaya
accident
myininaya
  • myininaya
u=cosx du=-sinx dx
anonymous
  • anonymous
:)
anonymous
  • anonymous
good....:
myininaya
  • myininaya
you want to try one i made up? its not hard
anonymous
  • anonymous
ok
myininaya
  • myininaya
\[\int\limits_{}^{}\frac{x+1}{x^2+2x}dx\]
anonymous
  • anonymous
ok.. let me try
anonymous
  • anonymous
u=x^2 + 2x du=2x+2 dx =2(x+1) dx so, 1/2du=x+1 dx
myininaya
  • myininaya
very good so far
anonymous
  • anonymous
1/2 integral of du/u =1/2 lnlul+c =1/2 ln/x^2+2xl+c
myininaya
  • myininaya
:)
anonymous
  • anonymous
yeaaaaaaaaaaaaa
anonymous
  • anonymous
i love this stuff
myininaya
  • myininaya
lol it is nice
myininaya
  • myininaya
\[\int\limits_{}^{}\frac{f'(x)}{f(x)}dx\] so when we have this what will out answer be in the form of?
anonymous
  • anonymous
f(x)*f'(x)
myininaya
  • myininaya
look at the one you just did didn't we have f'/f dx?
anonymous
  • anonymous
ohh... sorry.. yes yes
myininaya
  • myininaya
=ln|f(x)|+C
anonymous
  • anonymous
yes
myininaya
  • myininaya
\[\int\limits_{}^{}[f(x)]^n*f'(x)dx\] \[n \neq -1\] what about this? what will our answer be?
myininaya
  • myininaya
i will give you a hint let u=f(x) so du=f'(x) dx
anonymous
  • anonymous
jjajjjaj... nice hint
myininaya
  • myininaya
where are you from? you say jajaja alot lol
anonymous
  • anonymous
dominican republic
anonymous
  • anonymous
i am just laughing
myininaya
  • myininaya
jajaaja= laughing?
anonymous
  • anonymous
yess... how can i laugh??
myininaya
  • myininaya
its fine the way you type your laughter no worries i like it
anonymous
  • anonymous
lol
myininaya
  • myininaya
so this all makes a little more sense?
myininaya
  • myininaya
the integral stuff?
anonymous
  • anonymous
why?
myininaya
  • myininaya
im asking do you get the integral stuff better?
anonymous
  • anonymous
ohhhhhh,, yess
myininaya
  • myininaya
good :) im fixing to go to sleep goodnight
anonymous
  • anonymous
for me is mornig.. but good nigth,,,
myininaya
  • myininaya
good morning* i didn't sleep all night lol
anonymous
  • anonymous
jajajajaaja
anonymous
  • anonymous
ayayay.. no good
anonymous
  • anonymous
thank u very much...
myininaya
  • myininaya
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
myininaya
  • myininaya
later
anonymous
  • anonymous
ok,, thanks

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