Evaluate the integral $$\int\limits_{}^{}x/\sqrt{1-x^4}$$

Question

anonymous · Answer

$$\frac{\text{ArcSin}\left[x^2\right]}{2}+c  $$

myininaya · Answer

triangle problem!

myininaya · Answer

well there are formulas you can use
but i like using a right triangle for this

myininaya · Answer

let cos(theta)=x^2

anonymous · Answer

gotta use trig sub i think but i get cot

myininaya · Answer

attachment

zarkon · Answer

did you try myinimaya's substitution?

or $$\sin(\theta)=x^2$$

both will work

myininaya · Answer

yes both will like totally work :)

myininaya · Answer

if you giveup look at my attachment

anonymous · Answer

wow u make it look so easy

zarkon · Answer

the smart ones do that

myininaya · Answer

i like not remembering those formulas for this 
in fact i don't remember them
so i do a substitution for these all the time

anonymous · Answer

there is another nice one for you

anonymous · Answer

anonymous · Answer

@cinnamon, you know the best way to do them (besides computer algebra system like wolfram)?

anonymous · Answer

look in the back of the text they have all the formulas there

anonymous · Answer

back cover. i bet  i can find this one

anonymous · Answer

ok i am still looking but i bet it is here

anonymous · Answer

ok i can't find it. but before you do a trig sub try a u-sub 
$$u=x^2$$
$$du=2xdx$$ to get 

$$\frac{1}{2}\int \frac{du}{\sqrt{1-u^2}}$$

anonymous · Answer

i gotta write this stuff out for my final

anonymous · Answer

this gets 
$$\frac{1}{2}\sin^{-1}(u)$$ right away

anonymous · Answer

so answer is 
$$\frac{1}{2}\sin^{-1}(x^2)$$