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  • Identical expressions

  • sixteen *sin^2x*cos^6x
  • 16 multiply by sinus of squared x multiply by co sinus of e of to the power of 6x
  • sixteen multiply by sinus of squared x multiply by co sinus of e of to the power of 6x
  • 16*sin2x*cos6x
  • 16*sin²x*cos⁶x
  • 16*sin to the power of 2x*cos to the power of 6x
  • 16sin^2xcos^6x
  • 16sin2xcos6x
  • 16*sin^2x*cos^6xdx
Solving integrals/ 16*sin^2x*cos^6x

Integral of 16*sin^2x*cos^6x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                      
  /                      
 |                       
 |        2       6      
 |  16*sin (x)*cos (x) dx
 |                       
/                        
0
$$\int\limits_{0}^{\pi} 16 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}\, dx$$ 
Integral((16*sin(x)^2)*cos(x)^6, (x, 0, pi))
The answer (Indefinite) [src] 
  /                                                                                                                                                                                                        
 |                                  7                    8             8           7                   3       5            5       3             2       6             6       2              4       4   
 |       2       6             5*cos (x)*sin(x)   5*x*cos (x)   5*x*sin (x)   5*sin (x)*cos(x)   55*cos (x)*sin (x)   73*cos (x)*sin (x)   5*x*cos (x)*sin (x)   5*x*cos (x)*sin (x)   15*x*cos (x)*sin (x)
 | 16*sin (x)*cos (x) dx = C - ---------------- + ----------- + ----------- + ---------------- + ------------------ + ------------------ + ------------------- + ------------------- + --------------------
 |                                    8                8             8               8                   24                   24                    2                     2                     4          
/
$$\int 16 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}\, dx = C + \frac{5 x \sin^{8}{\left(x \right)}}{8} + \frac{5 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{15 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{5 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{2} + \frac{5 x \cos^{8}{\left(x \right)}}{8} + \frac{5 \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{55 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{24} + \frac{73 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{24} - \frac{5 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{8}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
5*pi
----
 8
$$\frac{5 \pi}{8}$$ 
=
= 
5*pi
----
 8
$$\frac{5 \pi}{8}$$ 
5*pi/8
Numerical answer [src] 
1.96349540849362
1.96349540849362

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

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