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cos^2x/sin^7x
Solving integrals/ cos^2x/sin^7x

Integral of cos^2x/sin^7x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     2      
 |  cos (x)   
 |  ------- dx
 |     7      
 |  sin (x)   
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/             
0
∫01cos⁡2(x)sin⁡7(x) dx\int\limits_{0}^{1} \frac{\cos^{2}{\left(x \right)}}{\sin^{7}{\left(x \right)}}\, dx 
Integral(cos(x)^2/sin(x)^7, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                  
 |                                                                                                   
 |    2                                                              3                      5        
 | cos (x)          log(-1 + cos(x))   log(1 + cos(x))        - 8*cos (x) - 3*cos(x) + 3*cos (x)     
 | ------- dx = C - ---------------- + --------------- - --------------------------------------------
 |    7                    32                 32                      4            6             2   
 | sin (x)                                               -48 - 144*cos (x) + 48*cos (x) + 144*cos (x)
 |                                                                                                   
/
∫cos⁡2(x)sin⁡7(x) dx=C−3cos⁡5(x)−8cos⁡3(x)−3cos⁡(x)48cos⁡6(x)−144cos⁡4(x)+144cos⁡2(x)−48−log⁡(cos⁡(x)−1)32+log⁡(cos⁡(x)+1)32\int \frac{\cos^{2}{\left(x \right)}}{\sin^{7}{\left(x \right)}}\, dx = C - \frac{3 \cos^{5}{\left(x \right)} - 8 \cos^{3}{\left(x \right)} - 3 \cos{\left(x \right)}}{48 \cos^{6}{\left(x \right)} - 144 \cos^{4}{\left(x \right)} + 144 \cos^{2}{\left(x \right)} - 48} - \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{32} + \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{32}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902e28-1e28
Plot the graph f(x)
The answer [src] 
     pi*I
oo - ----
      32
∞−iπ32\infty - \frac{i \pi}{32} 
=
= 
     pi*I
oo - ----
      32
∞−iπ32\infty - \frac{i \pi}{32} 
oo - pi*i/32
Numerical answer [src] 
6.88049276860284e+113
6.88049276860284e+113
The graph
Integral of cos^2x/sin^7x dx

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

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