thank you in advance.

box x is actually dx

is the ans   + 1/2log - 1/ + 1

  == / x dx

now put  X²+1=t²

2X dx=2tdt

Xdx=tdt

x=

integral becomes

==t/ x t dt/

== t² dt/t²-1

== t²+1-1 dt/t²-1

== 1 + 1/t²-1

the second part is a std integral

so we get the ans as

  + 1/2log - 1/ + 1  +

Yes, your answer is correct :)

Thank a lot!

put x=cot t

integral bcoms

= - sec t * cosec t * cot t dt

= - cosec ^2 t dt

= cot t

=x