Integration failure
08-21-2016, 10:14 PM
Post: #1
 lrdheat Senior Member Posts: 856 Joined: Feb 2014
Integration failure
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.
08-21-2016, 10:23 PM
Post: #2
 lrdheat Senior Member Posts: 856 Joined: Feb 2014
RE: Integration failure
...that is, when made into a definite integral!
08-22-2016, 03:50 AM
Post: #3
 Joe Horn Senior Member Posts: 2,001 Joined: Dec 2013
RE: Integration failure
(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.

<0|ɸ|0>
-Joe-
08-22-2016, 06:09 AM
Post: #4
 parisse Senior Member Posts: 1,311 Joined: Dec 2013
RE: Integration failure
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).
08-22-2016, 08:30 AM
Post: #5
 Werner Senior Member Posts: 865 Joined: Dec 2013
RE: Integration failure
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

41CV†,42S,48GX,49G,DM42,DM41X,17BII,15CE,DM15L,12C,16CE
08-22-2016, 10:20 AM
Post: #6
 Aries Member Posts: 159 Joined: Oct 2014
RE: Integration failure
(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 :-)
08-22-2016, 12:27 PM
Post: #7
 Marcel Member Posts: 177 Joined: Mar 2014
RE: Integration failure
Hi!

This is what I get (with 10077).

Irdheat is OK.

Marcel.

Attached File(s) Thumbnail(s)

08-22-2016, 04:07 PM
Post: #8
 Tim Wessman Senior Member Posts: 2,293 Joined: Dec 2013
RE: Integration failure
Xcas also behaves the same. Thanks!

TW

Although I work for HP, the views and opinions I post here are my own.
08-22-2016, 06:14 PM
Post: #9
 parisse Senior Member Posts: 1,311 Joined: Dec 2013
RE: Integration failure
Then you can solve it with trigtan
a:=int(ln(tan(x))/(sin(x)*cos(x))); trigtan(a)
08-24-2016, 08:30 PM
Post: #10
 roadrunner Senior Member Posts: 443 Joined: Jun 2015
RE: Integration failure
Don't know if this is related or not but ∫(ln(tan(x)),x) returns the following screen shot:

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.