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  • Identical expressions

  • ((sin(4x)- one)^ five)*cos(4x)
  • (( sinus of (4x) minus 1) to the power of 5) multiply by co sinus of e of (4x)
  • (( sinus of (4x) minus one) to the power of five) multiply by co sinus of e of (4x)
  • ((sin(4x)-1)5)*cos(4x)
  • sin4x-15*cos4x
  • ((sin(4x)-1)⁵)*cos(4x)
  • ((sin(4x)-1)^5)cos(4x)
  • ((sin(4x)-1)5)cos(4x)
  • sin4x-15cos4x
  • sin4x-1^5cos4x
  • ((sin(4x)-1)^5)*cos(4x)dx

  • Similar expressions

  • ((sin(4x)+1)^5)*cos(4x)
Solving integrals/ ((sin(4x)-1)^5)*cos(4x)

Integral of ((sin(4x)-1)^5)*cos(4x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                            
  /                            
 |                             
 |                5            
 |  (sin(4*x) - 1) *cos(4*x) dx
 |                             
/                              
0
$$\int\limits_{0}^{1} \left(\sin{\left(4 x \right)} - 1\right)^{5} \cos{\left(4 x \right)}\, dx$$ 
Integral((sin(4*x) - 1)^5*cos(4*x), (x, 0, 1))
The graph
Plot the graph f(x)
The answer [src] 
       3         5                  6           2           4   
  5*sin (4)   sin (4)   sin(4)   sin (4)   5*sin (4)   5*sin (4)
- --------- - ------- - ------ + ------- + --------- + ---------
      6          4        4         24         8           8
$$\frac{\sin^{6}{\left(4 \right)}}{24} - \frac{\sin^{5}{\left(4 \right)}}{4} - \frac{\sin{\left(4 \right)}}{4} + \frac{5 \sin^{4}{\left(4 \right)}}{8} + \frac{5 \sin^{2}{\left(4 \right)}}{8} - \frac{5 \sin^{3}{\left(4 \right)}}{6}$$ 
=
= 
       3         5                  6           2           4   
  5*sin (4)   sin (4)   sin(4)   sin (4)   5*sin (4)   5*sin (4)
- --------- - ------- - ------ + ------- + --------- + ---------
      6          4        4         24         8           8
$$\frac{\sin^{6}{\left(4 \right)}}{24} - \frac{\sin^{5}{\left(4 \right)}}{4} - \frac{\sin{\left(4 \right)}}{4} + \frac{5 \sin^{4}{\left(4 \right)}}{8} + \frac{5 \sin^{2}{\left(4 \right)}}{8} - \frac{5 \sin^{3}{\left(4 \right)}}{6}$$ 
-5*sin(4)^3/6 - sin(4)^5/4 - sin(4)/4 + sin(4)^6/24 + 5*sin(4)^2/8 + 5*sin(4)^4/8
Numerical answer [src] 
1.18330599393442
1.18330599393442

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

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