Mister Exam

Other calculators

sinxdx/(1-cosx)^3

  • How to use it?

  • Integral of d{x}:
  • Integral of xe Integral of xe
  • Integral of 3x² Integral of 3x²
  • Integral of e^-t Integral of e^-t
  • Integral of e^(x*y)

  • Identical expressions

  • sinxdx/(one -cosx)^ three
  • sinus of xdx divide by (1 minus co sinus of e of x) cubed
  • sinus of xdx divide by (one minus co sinus of e of x) to the power of three
  • sinxdx/(1-cosx)3
  • sinxdx/1-cosx3
  • sinxdx/(1-cosx)³
  • sinxdx/(1-cosx) to the power of 3
  • sinxdx/1-cosx^3
  • sinxdx divide by (1-cosx)^3

  • Similar expressions

  • sinxdx/(1+cosx)^3
Solving integrals/ sinxdx/(1-cosx)^3

Integral of sinxdx/(1-cosx)^3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                          
  /                          
 |                           
 |                 1         
 |  sin(x)*1*------------- dx
 |                       3   
 |           (1 - cos(x))    
 |                           
/                            
pi                           
--                           
2
$$\int\limits_{\frac{\pi}{2}}^{\pi} \sin{\left(x \right)} 1 \cdot \frac{1}{\left(- \cos{\left(x \right)} + 1\right)^{3}}\, dx$$ 
Integral(sin(x)*1/(1 - cos(x))^3, (x, pi/2, pi))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. 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:

    Method #2

    1. Rewrite the integrand:

    2. Rewrite the integrand:

    3. 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:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                        
 |                                                         
 |                1                           1            
 | sin(x)*1*------------- dx = C - ------------------------
 |                      3                              2   
 |          (1 - cos(x))           2 - 4*cos(x) + 2*cos (x)
 |                                                         
/
$$-{{1}\over{2\,\left(1-\cos x\right)^2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
3/8
$$\frac{3}{8}$$ 
=
= 
3/8
$$\frac{3}{8}$$
Simplify
Numerical answer [src] 
0.375
0.375
The graph
Integral of sinxdx/(1-cosx)^3 dx

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

    © Mister Exam – Calculator