I need some help with integrating {1 dx / (x^2+3)^(3/2) }. I got
(1/3)[ln {(x^2+3)^(1/2) +x} - ln {(3)^(1/2)}] + C. I tried to differentiate this but could not get it back to original form.
I am going to do this in a strange way:
Instead find,
Use substitution,
With
Thus,
Thus,
Apparently this can also be done with inverse hyperbolic functions, but I think it is a waste to memorize them. So I did it the standard way.
Now given,
Use the substitution and above work to get:
Use the properties of the natural logarithm,
Combine constants,