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Solving integrals/ (1/sin²x-4x)

Integral of (1/sin²x-4x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  0                   
  /                   
 |                    
 |  /   1         \   
 |  |------- - 4*x| dx
 |  |   2         |   
 |  \sin (x)      /   
 |                    
/                     
pi
$$\int\limits_{\pi}^{0} \left(- 4 x + \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx$$ 
Integral(1/(sin(x)^2) - 4*x, (x, pi, 0))
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. The integral of is when :

      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         \             2   cos(x)
 | |------- - 4*x| dx = C - 2*x  - ------
 | |   2         |                 sin(x)
 | \sin (x)      /                       
 |                                       
/
$$\int \left(- 4 x + \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx = C - 2 x^{2} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-oo
$$-\infty$$ 
=
= 
-oo
$$-\infty$$ 
-oo
Numerical answer [src] 
-4.39812420049212e+18
-4.39812420049212e+18

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

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