Integration (1 Viewer)

[Petyo]

Hi everyone, how would you do this question??
Find the integral S dx/ [x^2 . squrt of (x^2 +1 )]
My apologies I don't know how to use codes

 

[Timothy.Siu]

Hi everyone, how would you do this question??
Find the integral S dx/ [x^2 . squrt of (x^2 +1 )]
My apologies I don't know how to use codes

sub in x=tan @

dx=sec^2 @ d@

S sec²@d@/tan²@ (sec @)
=S sec@d@/tan²@
=S cos@d@/sin²@
=-1/sin@=-cosec@=root(x^2+1)/x

 

[Petyo]

Thanks but can you find any other way? because after substituting x=tanA and simpifiying, I have to substitute again sinA=u which makes the final anwer look... not really nice O_O.
I got 1/ sin (tan^-1 x) Correct me if I'm wrong

 

[Drongoski]

Edit

Misread question & did a different integration ! Well just treat that as a bonus solution.

 

[Timothy.Siu]

Thanks but can you find any other way? because after substituting x=tanA and simpifiying, I have to substitute again sinA=u which makes the final anwer look... not really nice O_O.
I got 1/ sin (tan^-1 x) Correct me if I'm wrong

yeah thats right, its not too long, u dont have to substitute sinA=u.

S cos@d@/sin^2 @ = S d(sin@)/sin^2 @ = -1/sin@

 

[Petyo]

The answer in the textbook is [squrt of(x^2 +1 )]/x.

 

[GUSSSSSSSSSSSSS]

hmm yes that just comes from substituting theta for x

doing that by drawing a triangle in which tan@ = x

etc etc...im sure you know the method