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Cunicularius

Calculus 2: Methods of Integration

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I've been wondering myself why I couldn't figure out how to do this integration.  Knowing now it has to do with trig, this problem can fuck right off.

you just have to use sin^2+cos^2=1

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You can use partial fractions to get it all in the numerator. 

Tried that, didn't get me anywhere, literally led me in a circle.

 

EDIT: Literally, gave me the same thing back I started with. Idk, maybe I did something wrong... its repeating , non-reducible, right?

9W9slXK.jpg

 

Trig substitution

 

x = tan(θ) 

dx = sec^2(θ)dθ

 

should leave you with

 

integral ( 1/sec^3(θ) ) 

which is integral ( cos^3(θ) ) 

 

integrate that using trig rules and substitute x in 

I'll try that.

 

Cuni doing math:

Spencer, PLS

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WOW, so I finally have my solution together!

 

It took a while to figure out... I had to go back and go over integration by parts again, and look at the different ways you can make formulas with it we've already gone over in class.

Got stuck a few times but after a while I actually got it, holy shit! 8D

3HK1dma.jpg?1tHZitw5.jpg?1

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ITS NOT THAT BAD, IS IT? 8C

 

It's bad enough that I wouldn't be able to do calculations with it unless I rewrote it, but then again, it usually takes me 3 or 4 attempts to write equations because I want them to be beautiful.

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Fak you cuni

<3

It's bad enough that I wouldn't be able to do calculations with it unless I rewrote it, but then again, it usually takes me 3 or 4 attempts to write equations because I want them to be beautiful.

Yeah, I know that feel... >~>

I can try to rewrite it...

EDIT: nvm, i dont have the patience right now

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Recommendation: in LaTeX, use \left( and \right) instead of just ( and ) when you're putting them around large (tall) expressions. It's probably also a good habit to put every expression into braces so that the \left( and \right) brackets don't end up mismatched.

 

Also, you have too many )s in a few of those.

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