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  • Identical expressions

  • cos^ eight (8x)/sin^ three (8x)
  • co sinus of e of to the power of 8(8x) divide by sinus of cubed (8x)
  • co sinus of e of to the power of eight (8x) divide by sinus of to the power of three (8x)
  • cos8(8x)/sin3(8x)
  • cos88x/sin38x
  • cos⁸(8x)/sin³(8x)
  • cos to the power of 8(8x)/sin to the power of 3(8x)
  • cos^88x/sin^38x
  • cos^8(8x) divide by sin^3(8x)
  • cos^8(8x)/sin^3(8x)dx
Solving integrals/ cos^8(8x)/sin^3(8x)

Integral of cos^8(8x)/sin^3(8x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  0             
  /             
 |              
 |     8        
 |  cos (8*x)   
 |  --------- dx
 |     3        
 |  sin (8*x)   
 |              
/               
0
$$\int\limits_{0}^{0} \frac{\cos^{8}{\left(8 x \right)}}{\sin^{3}{\left(8 x \right)}}\, dx$$ 
Integral(cos(8*x)^8/sin(8*x)^3, (x, 0, 0))
The answer (Indefinite) [src] 
  /                                                                                                                         
 |                                                                                                                          
 |    8                                                      3           5                                                  
 | cos (8*x)          7*log(-1 + cos(8*x))   3*cos(8*x)   cos (8*x)   cos (8*x)   7*log(1 + cos(8*x))         cos(8*x)      
 | --------- dx = C - -------------------- - ---------- - --------- - --------- + ------------------- + --------------------
 |    3                        32                8            12          40               32             /          2     \
 | sin (8*x)                                                                                            8*\-2 + 2*cos (8*x)/
 |                                                                                                                          
/
$$\int \frac{\cos^{8}{\left(8 x \right)}}{\sin^{3}{\left(8 x \right)}}\, dx = C - \frac{7 \log{\left(\cos{\left(8 x \right)} - 1 \right)}}{32} + \frac{7 \log{\left(\cos{\left(8 x \right)} + 1 \right)}}{32} - \frac{\cos^{5}{\left(8 x \right)}}{40} - \frac{\cos^{3}{\left(8 x \right)}}{12} - \frac{3 \cos{\left(8 x \right)}}{8} + \frac{\cos{\left(8 x \right)}}{8 \left(2 \cos^{2}{\left(8 x \right)} - 2\right)}$$
Simplify
The answer [src] 
0
$$0$$ 
=
= 
0
$$0$$ 
0
Numerical answer [src] 
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0.0

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

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