Can I get the hardest integrals you have...

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Can I get the hardest integrals you have to study calc 1?

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>>7770659

[math] \int\limits_\mathbb{R} {{e^{ - {x^2}}}dx} [/math]

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>>7770664

Note that this (and many other integrals) can be determined using dimensional analysis. I recommend the book "Street Fighting Mathematics" (its free google it) for that and many more useful techniques.

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>>7770659

[math]\int{ \frac {(1+x^2)dx} { (1-x^2) \sqrt {1+x^4 }}}[/math]

Not an easy integral.

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Find the first integral of (x * arctan(x^2))

The hardest you'll find for anyone in calc 1 because inverse trigonometric derivatives and integrals bridge into calc 2.

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>>7770684

I'll one up you with a shorter and still reasonable problem.

[math]\int { \sqrt { \tan{x} } dx } [/math]

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>>7770690

Also, here's the step by step process for this.

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>>7770695

This is exactly why its not a reasonable problem.

I could imagine seeing that in calc 2 for a take home problem to test yourself.

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>>7770695

wtf

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>>7770695

Easier way.

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>>7770659

Compute primitive of 1/sin x, that's fun as far as I remember

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>>7770659

Strange, I started integrals in Cal 2

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If you can't solve at least one of these your calc 1 course is unrigorous and you should find a better learning resource

[math] \int_0^\infty \frac{1+(\frac{x}{b+1})^2}{1+(\frac{x}{a})^2}\frac{1+(\frac{x}{b+2})^2}{1+(\frac{x}{a+1})^2}\cdots dx [/math]

[math] \int_0^a e^{-x^2} dx [/math]

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>>7770817

[math] \int_0^\infty \frac { 1+(\frac { x } { b+1 } )^2 } { 1+(\frac { x } { a } )^2 } \frac { 1+(\frac { x } { b+2 } )^2 } { 1+(\frac { x } { a+1 } )^2 } \cdots dx [/math]

Ftfy, (\frac {} {} not \frac{}{})

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>>7770820

Thanks, I checked my brackets like 3 times after...

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>>7770659

The indefinite integral of egg is chickhen + constant

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>>7770825

Protip, whenever you do anything in LaTeX here, just open up wordpad (which I'm pretty sure comes with all windows computers) paste your code, press replace, "{"->" { " & "}:->" } " It doesn't really matter how many spaces. I'll actually test below if it accepts 20 spaces.

[math]\frac { \tau \epsilon \sigma \tau } { \tau \epsilon \sigma \tau } [/math]

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>>7770844

Or just test it with LaTeX locally?

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>>7771014

/sci/ can't do \frac{}{}, and also \sqrt{} sometimes messes up without spaces, so do some other functions. That was the point of my post.

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OP here, is there a guide or book to learn integrals apart from this?

>>7770669

I'll take a look at that as well of course.

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Integrate [math]\displaystyle {1 \over \sqrt{2\pi}}\int e^{-x^2/2}\,dx[/math]

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>>7771120

"Calculus made easy" is a great book to start calculus with. I would then recommend you move on to Series immediately and understand integration and differentiation from the lens of Series (the relation between the exponential, polynomial and trigonometric functions is truly a thing of beauty). Finally, as a last step you should look at the geometric foundations of calculus (e.g try deriving the trig derivatives using only geometry).

Also don't forget that calculus like anything else, is only a tool. Never use a sledgehammer where a screwdriver will do.

Good luck.

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>>7771280

What about Granville? Also, what do you recommend for excercises?

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>>7771284

Can't speak for Granville as I've never read it myself. However from a quick browse online, it reads a bit denser then "Calc made easy". I recommend "Calc made easy" because its very short and gets straight to the point.

If you find you need to brush up on algebra and trig before tackling calc, I can recommend Pre-calculus by Axler.

Finally for exercises, I personally used the sample tests/problem sets on the MITocw course for calculus. Stewart's Calculus also has good problem sets. Whatever you decide to use, make sure you have the solutions to the problems readily available. This is probably the most important part, because you don't want any mistakes or misconceptions to compound.

Good luck.

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>>7771302

Thanks pal.

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>>7771259

gonna need some limits on that integral, buddy boy

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>>7770659

Integral of egg with respect to what, anon?

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Barnett Triple Integrals

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>>7771881

Well, Hen = Egg dx, so x.

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Elementary, my dear Watson.

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>>7770800

what did you do in calc1? lol

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>>7772325

theory of calculus?

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>>7771259

top kek

you don't need calculus for this baby

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>>7771259

well if you've done some stats it's easy to know the answer but the derivation of it is not that simple

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>>7771280

>never use a sledgehammer where a screwdriver will do

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>>7770659

x^x

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>>7773197

>Unfortunately FLT is not strong enough to prove √2 irrational

Every time

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