integrate dx/tanxcos^2x
sinx=u and du=cosxdx and dxcosx/sinxcos^2x then du/u(1-u)^2
1/u+1/1-u+1/1+u
a/u + b/1-u + c/1+u
I found c=-1/2, a=1 and b=1/2
ln|u|+1/2ln|1-u|-1/2ln|1+u|
ln|sinx|+1/2ln|1-sinx|-1/2ln|1+sinx|
ln|sinx|+ln|1-sinx|/1/2ln|1+sinx|
and I got stuck here.How can I solve that?
Then why did you ask for help?
Also, why don't you learn to post in a readable format.
Here is what you actually posted .
But it appears that is not what you mean, If so, learn to use grouping symbols.
Now note that
If you do not recognize at once that as a logarithm, then you are crippled by u-substitutions.
This is very difficult to read! Please use lots of parentheses to make your meaning clear.
For example, "b/1- u" would, strictly, be read "b- u" but I am sure you mean b/(1- u).
A typo. You mean ln|sin(x)|+ (1/2)ln(|1- sin(x)|)- (1/2)ln(|1+ sin(x)|)
What do you mean by "solve" it? You were asked to find an integral and you have. I presume you mean "simplify it" or write it in a simpler form. To do that use the laws of logarithms:and I got stuck here.How can I solve that?
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