Integral 1/(x^2 * sqrt(x^2 + 4)) should be (-sqrt(x^2 + 4))/4*x

The prime gives (-x -sqrt(x^2 + 4))/4*x after factorizing or after simplifying. Is this a bug?

Version 2016 04 14 (10077)

When integrating over a specific range such as pi/6 to pi/4, the exact answer converts to a correct approximate answer of ~.303

Am I missing something?

(07-31-2016 09:06 PM)lrdheat Wrote: [ -> ]Integral 1/(x^2 * sqrt(x^2 + 4)) should be (-sqrt(x^2 + 4))/4*x

The prime gives (-x -sqrt(x^2 + 4))/4*x after factorizing or after simplifying. Is this a bug?

No, because antiderivatives are defined up to a constant.

I must be math challenged/rusty...is not the "-x" that Prime produced a variable? How are the 2 answers equivalent?

What has me befuddled is that when made into a definite integral, Prime reports a correct answer.

(08-01-2016 10:08 PM)lrdheat Wrote: [ -> ]I must be math challenged/rusty...is not the "-x" that Prime produced a variable? How are the 2 answers equivalent?

If you simplify the Prime result...

Code:

` –x – sqrt(x²+4)`

---------------

4x

–x sqrt(x²+4)

= -- – ----------

4x 4x

sqrt(x²+4)

= –1/4 – ----------

4x

sqrt(x²+4)

= const – ----------

4x

...you get the same antiderivative plus a constant.

Dieter

Thanks!

For some reason, I was seeing the denominator as "4" instead of "4*x".