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Solving integrals/ sinx/(3cosx-1)^3

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

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |       sin(x)       
 |  --------------- dx
 |                3   
 |  (3*cos(x) - 1)    
 |                    
/                     
0
∫01sin⁡(x)(3cos⁡(x)−1)3 dx\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\left(3 \cos{\left(x \right)} - 1\right)^{3}}\, dx 
Integral(sin(x)/(3*cos(x) - 1)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                   
 |                                                    
 |      sin(x)                          1             
 | --------------- dx = C + --------------------------
 |               3                                2   
 | (3*cos(x) - 1)           6 - 36*cos(x) + 54*cos (x)
 |                                                    
/
∫sin⁡(x)(3cos⁡(x)−1)3 dx=C+154cos⁡2(x)−36cos⁡(x)+6\int \frac{\sin{\left(x \right)}}{\left(3 \cos{\left(x \right)} - 1\right)^{3}}\, dx = C + \frac{1}{54 \cos^{2}{\left(x \right)} - 36 \cos{\left(x \right)} + 6}
Simplify
The answer [src] 
  1                1             
- -- + --------------------------
  24                         2   
       6 - 36*cos(1) + 54*cos (1)
−124+1−36cos⁡(1)+6+54cos⁡2(1)- \frac{1}{24} + \frac{1}{- 36 \cos{\left(1 \right)} + 6 + 54 \cos^{2}{\left(1 \right)}} 
=
= 
  1                1             
- -- + --------------------------
  24                         2   
       6 - 36*cos(1) + 54*cos (1)
−124+1−36cos⁡(1)+6+54cos⁡2(1)- \frac{1}{24} + \frac{1}{- 36 \cos{\left(1 \right)} + 6 + 54 \cos^{2}{\left(1 \right)}} 
-1/24 + 1/(6 - 36*cos(1) + 54*cos(1)^2)
Numerical answer [src] 
0.390643802434533
0.390643802434533

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

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