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  • Identical expressions

  • (one /(sin^ three (x)cos^ five (x)))dx
  • (1 divide by ( sinus of cubed (x) co sinus of e of to the power of 5(x)))dx
  • (one divide by ( sinus of to the power of three (x) co sinus of e of to the power of five (x)))dx
  • (1/(sin3(x)cos5(x)))dx
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Solving integrals/ (1/(sin^3(x)cos^5(x)))dx

Integral of (1/(sin^3(x)cos^5(x)))dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |     3       5      
 |  sin (x)*cos (x)   
 |                    
/                     
x
$$\int\limits_{x}^{x} \frac{1}{\sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}\, dx$$ 
Integral(1/(sin(x)^3*cos(x)^5), (x, x, x))
The answer (Indefinite) [src] 
  /                                                                                         
 |                                               /        2   \             2           4   
 |        1                                 3*log\-1 + cos (x)/   -1 - 3*cos (x) + 6*cos (x)
 | --------------- dx = C - 3*log(cos(x)) + ------------------- + --------------------------
 |    3       5                                      2                    4           6     
 | sin (x)*cos (x)                                                 - 4*cos (x) + 4*cos (x)  
 |                                                                                          
/
$$\int \frac{1}{\sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}\, dx = C + \frac{3 \log{\left(\cos^{2}{\left(x \right)} - 1 \right)}}{2} - 3 \log{\left(\cos{\left(x \right)} \right)} + \frac{6 \cos^{4}{\left(x \right)} - 3 \cos^{2}{\left(x \right)} - 1}{4 \cos^{6}{\left(x \right)} - 4 \cos^{4}{\left(x \right)}}$$
Simplify
The answer [src] 
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$$0$$ 
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Numerical answer [src] 
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