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Saint Casanova

Saint Casanova

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Is there a simple way of solving this integral. I can’t find a suitable substitution to use and using parts just becomes extremely messy and ridiculous.
 

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is this college algevra?
 
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Why can't you just Google it m8
 
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Maybe you could let u= 1+x, so u-1=x,
x^2= (u-1)^2
Du/dx= 1
dx=1/du
And then you’ll have integral of ln(u-1+(1+(u-1)^2))du which you can try solving by parts ???
 
What is this for? Uni?
 
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Looks like you just have to do integration by parts, it works out fairly nicely
 
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Maybe you could let u= 1+x, so u-1=x,
x^2= (u-1)^2
Du/dx= 1
dx=1/du
And then you’ll have integral of ln(u-1+(1+(u-1)^2))du which you can try solving by parts ???
So the ones cancel and you get ln(u+(u-1)^2), so using by parts you have u= ln(u+(u-1)^2 and dv/du= 1.
 

Looks like you just have to do integration by parts, it works out fairly nicely
Does the substitution i used above make it a bit easier to solve. You still have to use parts either way.
 
Does the substitution i used above make it a bit easier to solve. You still have to use parts either way.
Probably not, you don't use regular integration by parts. You do the trick where one of the parts =1
 
Probably not, you don't use regular integration by parts. You do the trick where one of the parts =1
Yeah that’s what I did. Dv/dx= 1 so v= x
U= ln(u+(u-1)^2). Differentiating I would probably be quite annoying but it still should be easier, no ?
 

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