integral of sqrt(x^2+2x), trig substitution, calculus 2 tutorial.

integral of sqrt(x^2+2x), trig substitution, calculus 2 tutorial.
----------------------------------------
#blackpenredpen #math #calculus #apcalculus

[shaikhameerul]

that triple variable substitution was handled like a boss

[XXgamemaster]

I’m amazed how you can start with a fairly simple integrand and end up with a rather complicated solution.

[jemcel]

It's so cute and adorable when you say "u-world", "x-world", and "theta world" lol. Btw, you and PatrickJMT would make a great team in making math vids :)

[someperson]

You made a small copying error at the end of the computation (which I do all the time). The last term of the answer should be ln|x+1+sqrt(x^2+2x)|, since
x+1+sqrt(x^2+2x)<0, for x<=-2 and (-INF, -2] is in the domain of the integrand. I often recommend your videos to my students. Thanks for making them.

[Skandalos]

Im always amazed by what we can do in maths just through the application of rules and formulas, without understanding the meaning of any of the intermediate steps.

[kantaprasadsinha]

Your way of teaching is highly appreciated.

[Reasonably_Andy]

I know I am very late to the party on this one, but if I'm not mistaken don't you need to put an absolute value inside the natural log in the final solution? (x + 1 + sqrt(x^2+2x)) will be negative for all x < -2.

[angelcru]

that was the most straight answer I've ever seen in a math tutorial, just what I needed thanks :)

[vasudhagupta]

Anybody else just remember from highschool having learnt integration of √u²-1=u/2√u²-1 - 1/2ln|u+√u²-1| +C 😂

[eliasmazhukin]

Me: *does 300 substitutions and finally gets to the answer*
Me: Yes! Finally!
The 299 worlds I have to go back to: Are we jokes to you?

[Mihau_desu]

When x=-2, ln(x+1+sqrt(x^2+2x)) = ln(-2+1+sqrt(4-4))= ln(-1) so you actually need the abs. value

[loneranger]

There is a simplified version of it:

= (x+1)/2 * sqrt(x^2 + 2x) - 1/2 * cosh^-1(x+1)

[sssbbb]

This is the only problem in the exam that I cannot solve 😥

[puissantpoisson]

I could be missing something (I haven't actually really done integration since a while, and trig-wise I never used sec and the likes, only sin cos and tan), but at the 3:50 mark, if sec²(theta)-1 is equal to tan²(theta), taking the square root seems like it would return the absolute value of tan(theta).

Maybe it was for the sake of the explanation and it actually is tan(theta)?

[IhimbruBelloOngum]

Interesting, so what will be the solution to the integral of √ (1+4x²)

[charlietlo]

Hem... x+1+sqrt(x²+2x) > 0 only in IR{+} world. So the abs value is necessary in the final solution if you're working in entire IR world (if you erease it, you're juste assuming complexe values and so working in C world).

[arielfuxman]

Why did you allow yourself to write the square root of tan^2 theta as tan theta without the absolute value?

[davidgillies]

I always preferred the hyperbolic trig method because there's one less substitution.

[bahaloicperrial]

It is not the only possibility we can also have as answer 1/4(sh 2u)-1/2u

[RedRad]

I hope you don't get offended, bprp, but this haircut is "the most Chinese" one :P
I don't say you look bad though