Elementary integral problems

Question

astrophysics · Answer

|dw:1442388808400:dw|

astrophysics · Answer

http://puu.sh/kd3Dz/a5f1d4e81e.png if it's not clear enough

astrophysics · Answer

|dw:1442388847137:dw| so far...maybe these can be a little tricky

empty · Answer

Oooh damn nice. I think 21 is kinda famous, or at least it looks hard. I don't know about the other one if that one's gonna be easy or hard. I'm gonna guess you complete the square for that one or something.

astrophysics · Answer

Maybe I'll post solutions once I'm done all of them, just for fun

imqwerty · Answer

sry astro i i havent yet given the answer to that quadrilateral question :) i will do that after some time 2weeks ig :)  hehe :)

empty · Answer

Ah I just figured out 12 I think, but 21... Hmmm... I'll have to try IBP maybe but I'm kinda scared to lol

astrophysics · Answer

|dw:1442389097067:dw| part 2 http://puu.sh/kd3Qd/129ef4383c.png

astrophysics · Answer

Yeah try what ever one you like out lol

jhannybean · Answer

$$\sf \#12 \ \ \int \frac{x}{x^4+x^2+1}dx$$

astrophysics · Answer

Want to know how?

jhannybean · Answer

No, not yet

nincompoop · Answer

font looks familiar

jhannybean · Answer

You have an x at the top and you have different "variations" of x at the bottom

astrophysics · Answer

Stewart calc nin lol

jhannybean · Answer

Wouldnt a u-sub work?/

nincompoop · Answer

I know ... LOL

jhannybean · Answer

Like whats the easiest way of making the top a derivative of something? now I know you're either going to u-sub $\sf x^2$ and $\sf x^4$

astrophysics · Answer

Hint: $$\sf \#12 \ \ \int\limits \frac{x}{(x^2)^2+x^2+1}dx$$

jhannybean · Answer

OKAY!

nincompoop · Answer

omg why did you give a hint

jhannybean · Answer

$$ u=x^2~,~ du = 2xdx$$$$2\int\frac{du}{(u)^2+u+1}$$

astrophysics · Answer

$$\checkmark $$

nincompoop · Answer

LOLLLLL go jhanny go jhanny 
aren't you supposed to be doing chemistry?

jhannybean · Answer

.......... yeah

nincompoop · Answer

I am a sober now, so I can help

zzr0ck3r · Answer

good old Stewart

irishboy123 · Answer

#21
$\int arctan \sqrt{x} \,\, dx$

|dw:1442396993523:dw|

$\frac{1}{2}x^{-1/2}dx = 2 \tan \theta \sec^2 \theta \, d\theta $
$dx = 2 \tan \theta \ \sec^2 \theta \, d\theta $ [looking do-able already]
$\implies \int \theta . 2 \tan \theta \ \sec^2 \theta \, d\theta\,\, dx$ [parts]
$u = \theta, u' = 1, v'= 2 \tan \theta \ \sec^2, v = \tan^2 \theta   $

and that's most of it