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1/(sin^3x*cos^3x)

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  • 1/(sin^3x*cos^3x)dx
Solving integrals/ 1/(sin^3x*cos^3x)

Integral of 1/(sin^3x*cos^3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |     3       3      
 |  sin (x)*cos (x)   
 |                    
/                     
0
$$\int\limits_{0}^{1} \frac{1}{\sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx$$ 
Integral(1/(sin(x)^3*cos(x)^3), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                    
 |                                                                             2       
 |        1                    /        2   \                        -1 + 2*sin (x)    
 | --------------- dx = C - log\-1 + sin (x)/ + 2*log(sin(x)) - -----------------------
 |    3       3                                                        2           4   
 | sin (x)*cos (x)                                              - 2*sin (x) + 2*sin (x)
 |                                                                                     
/
$$\int \frac{1}{\sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx = C - \frac{2 \sin^{2}{\left(x \right)} - 1}{2 \sin^{4}{\left(x \right)} - 2 \sin^{2}{\left(x \right)}} - \log{\left(\sin^{2}{\left(x \right)} - 1 \right)} + 2 \log{\left(\sin{\left(x \right)} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
oo - pi*I
$$\infty - i \pi$$ 
=
= 
oo - pi*I
$$\infty - i \pi$$ 
oo - pi*i
Numerical answer [src] 
9.15365037903492e+37
9.15365037903492e+37
The graph
Integral of 1/(sin^3x*cos^3x) dx

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

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