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exravenBest ResponseYou've already chosen the best response.0
\[\int\limits \frac{x^4 + 1}{x^2 \sqrt{x^4  1}}dx\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\[u=x^41\] \[(u+1)^{1/4}=x\] \[\frac 14(u+1)^{3/4}\text du=\text dx\] \[\int\limits \frac{u+2}{(u+1)^{2/4} \sqrt{u}}\frac 14(u+1)^{3/4}\text du\]
 one year ago

exravenBest ResponseYou've already chosen the best response.0
I have already tried that substitution and stuck
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
maybe there is a trig substitution
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
\[\int\limits\frac{(x^{2})^{2}+1}{x^{2}\sqrt{(x^{2})^{2}1}} \] maybe a trig sub..u^2 = tan\theta or u^2 = sin\theta
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
i mean x^2 = tan\theta or x^2 = sin\theta
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
this is guessing game...maybe\[x^2=\sec u\]
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
yeah my bad..but i think x^2 = tan(u) would work as well..
 one year ago

exravenBest ResponseYou've already chosen the best response.0
here it is\[\int\limits \frac{\sec^2 u + 1}{2 \sqrt{\sec u}} du\]
 one year ago

exravenBest ResponseYou've already chosen the best response.0
I don't know what to do with the sqrt{sec u}
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
secx = 1/cosx maybe weirstrass substitution?
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
wait..wont work http://www.wolframalpha.com/input/?i=integrate+sqrt%28secx%29
 one year ago

exravenBest ResponseYou've already chosen the best response.0
there must be a tricky substitution
 one year ago

cruffoBest ResponseYou've already chosen the best response.0
Have you tried splitting the integral up like this: ?
 one year ago

exravenBest ResponseYou've already chosen the best response.0
it won't work... http://www.wolframalpha.com/input/?i=integrate+%28x^2%29%2F%28sqrt%28x^4+1%29%29+dx
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
then what about this \[\int\limits\frac{(secu)^{2}+1}{(secu)^{2}\sqrt{(secu)^{2}1}} *\frac{tanusecu}{2\sqrt{secu}} \]? its not going to look nice tho
 one year ago

exravenBest ResponseYou've already chosen the best response.0
\[\int\limits \frac{\sec^2 u+1}{2\sqrt{\sec u}} du\]
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
hmm..this is hard..would integration by parts work?
 one year ago

exravenBest ResponseYou've already chosen the best response.0
haven't tried that, but I doubt it will work
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
\[sec=\sqrt{tan^2+1}\]\[sec^2=tan^2+1\] \[\int\limits \frac{\tan^2 u+2}{2tan^2u+2} du\] or am i missing something?
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
my last hope is x=e^t
 one year ago

Mimi_x3Best ResponseYou've already chosen the best response.1
x=e^t? i might sound stupid; but where did e^t come from?
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
i missed something :)\[x^{1/4}\ne x\]
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
well maybe that will lead us to some sinh and cosh
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
x=e^t dx=e^t dt\[\int \frac{e^{4t} + 1}{e^{2t} \sqrt{e^{4t}  1}}e^t\text{d}t=\int \frac{e^{2t} + e^{2t}}{ \sqrt{e^{2t}  e^{2t}}}\text{d}t=\int \frac{2\cosh t}{\sqrt{\sinh t}} \text{d}t\]
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
OOoopS typo again\[\int \frac{2\cosh 2t}{\sqrt{2\sinh 2t}} \text{d}t\]
 one year ago

exravenBest ResponseYou've already chosen the best response.0
now I can rest peacefully lol
 one year ago
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