cos(x)-sin(x)/sin(x)+cos(x)?

Question

how can find the integrals of cos(x)-sin(x)/sin(x)+cos(x)?

Answer 1

The above solution is correct. You could also say that we need to perform the following u-substitution:

u = sin x + cos x
du = cos x - sin x.

After this substitution, the integrand becomes (1/u)du. You should know the integral of this! It's ln(u) + C. Plugging back in for u gives us the final answer:

ln ( sin x + cos x ) + C.

BTW, when you state a problem like this you should use parentheses and say

(cos x - sin x)/(sin x + cos x).

What you wrote actually says something different than what you probably *meant* to say.

Answer 2

U-substitution would work here:

Integral {dx * [cos(x)-sin(x)] / [sin(x)+cos(x)] }

u = sin(x) + cos(x) and du= cos(x) - sin(x) dx

So,
Integral {dx * [cos(x)-sin(x)] / [sin(x)+cos(x)] }
= Integral {du/u}
= ln u + C
=ln [sin(x) + cos(x)] + C

Answer 3

INTEGRAL OF [cos(x)-sin(x)/sin(x)+cos(x)]dx =
INTEGRAL OF [2cos(x)-1]dx =
-2sin(x) - x + C

Answer 4

put sin(x)+ cos(x) = y
dy/dx = cos(x) - sin(x)
so integral = ln Y + c
= lin(sin(x)+cos(x)) + c

Answer 5

integ ((cos x - sin x)/(sin x + cos x)).dx

Let t = sinx + cos x
dt = (cos x - sin x).dx

therefore, integ (dt/t)
= log t
= log (sinx + cos x)

Answer 6

kpt is right

Answer 7

you can use a calculator