How would I go about integrating 1/(1+2x^2) with substitution? Calculus question from r/askmath

Answering your question on Reddit, how to integrate 1/(1+2x^2) with substitution. Here's the original post: / eetd4tlrti
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[@soyanshumohapatra]

*Integration is more difficult than differentiation*

[@MitStudent-n6k]

But way more fun then differentiation 😅

[@adambomb1017]

How are you allowed to just change the two into sqrt(2)? sqrt(2) does not equal 2. I don't see how this is allowed.

[@guyonYTube]

Why can't you sub u = 1 + 2x^2 ? I get ln(1 + 2x^2)/4x if I do that

[@Megumin_Random]

Take the derivative of your answer, and I think you’ll find an issue

[@liwen9244]

Because we cannot divide a variable we can only divide a constnat

[@______7660]

Hello sir

[@sametyetimoglu6026]

I already knew the answer but I stopped by to drop a like because I wouldn't have known without your help in the past!

[@adw1z]

How would I solve 1+1+1 without using 1+1 = 2

[@bprpcalculusbasics]

3*1=3

[@nomooon]

​@@bprpcalculusbasics this is some Zen master stuff

[@hysterixation]

Finally a thumbnail where I solved it correctly before clicking on the video LOL

[@DefenderTerrarian]

Couldn't you also factor out a constant of 1/2, then use the generalized arctan integration formula?

[@matematicashowmaster3001]

😊😊😊

[@jam9339]

Could you just substitute x as 1/2tanθ

[@capnbug]

ay it was exactly how i thought youd do it

[@QuentinStephens]

Are you sure you're correct at 3:30? Doesn't the term external to the integral (1 / sqrt (2)) apply to the whole integral so you need to divide C by sqrt (2)? Or did you just forget a set of brackets?

[@henry55]

i’m not sure but i think you don’t need to because C can just be any number

[@______7660]

Sir I'm from India ❤

[@soyanshumohapatra]

Me too

[@alexdefoc6919]

How to prove 1/a^2+u^2 ?

[@qwepoi1972]

Divide top and bottom by a²

[@forcelifeforce]

*Why* would you think a^2 + u^2 is a denominator without writing grouping symbols around it!? You need to write it as 1/(a^2 + u^2), for example.