Indefinite integral of dx/(sin(x)+tan(x)
I replaced tan(x) with sin(x)/cos(x) so then I flipped the sinx/cosx term and wrote the integral as:
cosx/(sin(x) + sin(x) dx
becomes
cosx/(2 sinx) dx
Then I took the 1/2 out of the integral
1/2 times integral cos x / sin x dx
Let u = sin x du = cos x dx
1/2 times integral du / u
integrate
1/2 * ln u + C
replace sin x
1/2 * ln sin x + C
Is that correct?
And how do you do this with replacing sin x with 2u/ 1 + u^2 in the original problem and so on?
kind of hung up that way with the tangent function?
Thanks
There is a ")" missing in your first integral. Is this ?
If so then and multiplying both numerator and denominator by cos(x) gives , NOT what you have.
becomes
cosx/(2 sinx) dx
Then I took the 1/2 out of the integral
1/2 times integral cos x / sin x dx
Let u = sin x du = cos x dx
1/2 times integral du / u
integrate
1/2 * ln u + C
replace sin x
1/2 * ln sin x + C
Is that correct?
And how do you do this with replacing sin x with 2u/ 1 + u^2 in the original problem and so on?
kind of hung up that way with the tangent function?
Thanks