Question

integration of 1/x^4(x^2+1)^1/2

Answer 1

\[\int\limits \frac{ dx }{ x ^{4}\sqrt{x ^{2}+1} }\]

Answer 2

did you try to put x = tan u ?

Answer 3

you mean \[\tan \theta \] if so yes i tried

Answer 4

yeah, theta is not so convenient to write, so i used 'u' , or we can use 't'
x = tan t will simplify things, what is your new intergral in terms of t ?

Answer 5

\[\int\limits\frac{ \sec ^{2}\theta }{ \tan^4\theta \sec \theta }d \theta\]

Answer 6

it was \[\int\limits\frac{ \sec ^{2}\theta }{ \tan^4\theta \sqrt{\tan^2 \theta+1} }d \theta\]

Answer 7

i used \[\sqrt{x^2+1} =\sec \theta \]

Answer 8

yeah
so, sec t cot^4 t
since we have cot t
lets try to bring csc t

sec t * cot t = 1/cos t * cos t / sin t = csc t
so, it'll be
cot^3 t csc t dt

Answer 9

see if you get that ^

Answer 10

The attachment shows how Mathematica does it.

Answer 11

we don't need full solutions i think, if mostafa wants to learn...

Answer 12

yes and no

Answer 13

i will try to get what you said hartnn

Answer 14

finally i got it thanks

Answer 15

good! :)