HIGH IQ only

[Saint Casanova]

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.

 

[Deleted member 31155]

is this college algevra?

 

[Deleted member 31457]

Why can't you just Google it m8

 

[Saint Casanova]

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 ???

 

[Saint Casanova]

Why can't you just Google it m8

Google shows me something utterly ridiculous

 

[Deleted member 31457]

What is this for? Uni?

 

[mogger123]

integral of ln(x+sqrt(1+x^2))

Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step

www.symbolab.com

Looks like you just have to do integration by parts, it works out fairly nicely

 

[Saint Casanova]

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.

 

[Saint Casanova]

integral of ln(x+sqrt(1+x^2))

Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step

www.symbolab.com

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.

 

[Saint Casanova]

What is this for? Uni?

It’s technically A-level so around AP level ?

 

[mogger123]

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

 

[Saint Casanova]

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 ?

 

[Saint Casanova]

Il

 

[Saint Casanova]

tour to