Integration failure

[lrdheat]

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.

[lrdheat]

...that is, when made into a definite integral!

[Joe Horn]

(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.

[parisse]

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).

[Werner]

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

[Aries]

(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 :-)

[Marcel]

Hi!

This is what I get (with 10077).

Irdheat is OK.

Marcel.

[Tim Wessman]

Xcas also behaves the same. Thanks!

[parisse]

Then you can solve it with trigtan
a:=int(ln(tan(x))/(sin(x)*cos(x))); trigtan(a)

[roadrunner]

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.

-road

[parisse]

This is unrelated, but thanks for the bug report!