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Solving integrals/ cos(x)*ctg(x)*ctg(x)-sin(x)*ctg(x)

Integral of cos(x)*ctg(x)*ctg(x)-sin(x)*ctg(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  t                                          
  /                                          
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 |  (cos(x)*cot(x)*cot(x) - sin(x)*cot(x)) dx
 |                                           
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pi                                           
--                                           
2
$$\int\limits_{\frac{\pi}{2}}^{t} \left(- \sin{\left(x \right)} \cot{\left(x \right)} + \cos{\left(x \right)} \cot{\left(x \right)} \cot{\left(x \right)}\right)\, dx$$ 
Integral(cos(x)*cot(x)*cot(x) - sin(x)*cot(x), (x, pi/2, t))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    1. Don't know the steps in finding this integral.

      But the integral is

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                 
 |                                                   1              
 | (cos(x)*cot(x)*cot(x) - sin(x)*cot(x)) dx = C - ------ - 2*sin(x)
 |                                                 sin(x)           
/
$$-2\,\sin x-{{1}\over{\sin x}}$$
Simplify
The answer [src] 
      1              
3 - ------ - 2*sin(t)
    sin(t)
$$- 2 \sin{\left(t \right)} + 3 - \frac{1}{\sin{\left(t \right)}}$$ 
=
= 
      1              
3 - ------ - 2*sin(t)
    sin(t)
$$- 2 \sin{\left(t \right)} + 3 - \frac{1}{\sin{\left(t \right)}}$$
Упростить

    Use the examples entering the upper and lower limits of integration.

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