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+--- Thread: Integration failure (/thread-6716.html)
Integration failure - lrdheat - 08-21-2016 10:14 PM
Int (ln(tan(X)))/((sin(X))(cos(X))) returns the integral
TI NSpire returns ((ln(tan(X)))^2)/2
Both return same answer in approximate mode.
RE: Integration failure - lrdheat - 08-21-2016 10:23 PM
...that is, when made into a definite integral!
RE: Integration failure - Joe Horn - 08-22-2016 03:50 AM
(08-21-2016 10:14 PM)lrdheat Wrote: Int (ln(tan(X)))/((sin(X))(cos(X))) returns the integral
TI NSpire returns ((ln(tan(X)))^2)/2
Both return same answer in approximate mode.
Are you sure the parentheses in your input are correct? As shown, the integral ends before the division sign, which I suspect is not what you wanted.
RE: Integration failure - parisse - 08-22-2016 06:09 AM
If you derive (ln(tan(x)))^2, there should be a (1+tan(x)^2) term, but I don't see it in your input (which has strange parenthesis and missing * sign).
RE: Integration failure - Werner - 08-22-2016 08:30 AM
Hello Bernard.
Using 1+tan^2 = 1/cos^2,
the derivative of ((ln(tan(x))^2)/2 is ln(tan(x))/(sin(x)*cos(x)),
which is what I think the original poster meant.
I have no Prime to verify though.
Cheers, Werner
RE: Integration failure - Aries - 08-22-2016 10:20 AM
(08-21-2016 10:14 PM)lrdheat Wrote: Int (ln(tan(X)))/((sin(X))(cos(X))) returns the integral
TI NSpire returns ((ln(tan(X)))^2)/2
Both return same answer in approximate mode.
* is missing and parenthesis levels are "untidy" ;-)
Best,
Aries :-)
RE: Integration failure - Marcel - 08-22-2016 12:27 PM
Hi!
This is what I get (with 10077).
Irdheat is OK.
Marcel.
RE: Integration failure - Tim Wessman - 08-22-2016 04:07 PM
Xcas also behaves the same. Thanks!
RE: Integration failure - parisse - 08-22-2016 06:14 PM
Then you can solve it with trigtan
a:=int(ln(tan(x))/(sin(x)*cos(x))); trigtan(a)
RE: Integration failure - roadrunner - 08-24-2016 08:30 PM
Don't know if this is related or not but ∫(ln(tan(x)),x) returns the following screen shot:
[attachment=3848]
the denominator is +([TAN(x)^2 1]). The plus sign is located incorrectly but when you copy it onto the command line it is correct.
This is with 10077.
-road
RE: Integration failure - parisse - 08-25-2016 05:58 AM
This is unrelated, but thanks for the bug report!