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Solving integrals/ sin²(2x)cos²x

Integral of sin²(2x)cos²x dx

Limits of integration:

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The solution

You have entered [src] 
  1                     
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 |     2         2      
 |  sin (2*x)*cos (x) dx
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0
$$\int\limits_{0}^{1} \sin^{2}{\left(2 x \right)} \cos^{2}{\left(x \right)}\, dx$$ 
Integral(sin(2*x)^2*cos(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                   
 |                                              3     
 |    2         2             sin(4*x)   x   sin (2*x)
 | sin (2*x)*cos (x) dx = C - -------- + - + ---------
 |                               16      4       12   
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$$\int \sin^{2}{\left(2 x \right)} \cos^{2}{\left(x \right)}\, dx = C + \frac{x}{4} + \frac{\sin^{3}{\left(2 x \right)}}{12} - \frac{\sin{\left(4 x \right)}}{16}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   2       2         2       2         2       2         2       2           2                       2                       2                       2                 
cos (1)*cos (2)   cos (1)*sin (2)   cos (2)*sin (1)   sin (1)*sin (2)   7*cos (1)*cos(2)*sin(2)   cos (2)*cos(1)*sin(1)   sin (2)*cos(1)*sin(1)   sin (1)*cos(2)*sin(2)
--------------- + --------------- + --------------- + --------------- - ----------------------- + --------------------- + --------------------- + ---------------------
       4                 4                 4                 4                     24                       3                       6                       24
$$\frac{\sin^{2}{\left(1 \right)} \sin{\left(2 \right)} \cos{\left(2 \right)}}{24} + \frac{\cos^{2}{\left(1 \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)} \cos^{2}{\left(2 \right)}}{3} + \frac{\sin^{2}{\left(1 \right)} \cos^{2}{\left(2 \right)}}{4} - \frac{7 \sin{\left(2 \right)} \cos^{2}{\left(1 \right)} \cos{\left(2 \right)}}{24} + \frac{\sin^{2}{\left(2 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{\sin{\left(1 \right)} \sin^{2}{\left(2 \right)} \cos{\left(1 \right)}}{6} + \frac{\sin^{2}{\left(1 \right)} \sin^{2}{\left(2 \right)}}{4}$$ 
=
= 
   2       2         2       2         2       2         2       2           2                       2                       2                       2                 
cos (1)*cos (2)   cos (1)*sin (2)   cos (2)*sin (1)   sin (1)*sin (2)   7*cos (1)*cos(2)*sin(2)   cos (2)*cos(1)*sin(1)   sin (2)*cos(1)*sin(1)   sin (1)*cos(2)*sin(2)
--------------- + --------------- + --------------- + --------------- - ----------------------- + --------------------- + --------------------- + ---------------------
       4                 4                 4                 4                     24                       3                       6                       24
$$\frac{\sin^{2}{\left(1 \right)} \sin{\left(2 \right)} \cos{\left(2 \right)}}{24} + \frac{\cos^{2}{\left(1 \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)} \cos^{2}{\left(2 \right)}}{3} + \frac{\sin^{2}{\left(1 \right)} \cos^{2}{\left(2 \right)}}{4} - \frac{7 \sin{\left(2 \right)} \cos^{2}{\left(1 \right)} \cos{\left(2 \right)}}{24} + \frac{\sin^{2}{\left(2 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{\sin{\left(1 \right)} \sin^{2}{\left(2 \right)} \cos{\left(1 \right)}}{6} + \frac{\sin^{2}{\left(1 \right)} \sin^{2}{\left(2 \right)}}{4}$$ 
cos(1)^2*cos(2)^2/4 + cos(1)^2*sin(2)^2/4 + cos(2)^2*sin(1)^2/4 + sin(1)^2*sin(2)^2/4 - 7*cos(1)^2*cos(2)*sin(2)/24 + cos(2)^2*cos(1)*sin(1)/3 + sin(2)^2*cos(1)*sin(1)/6 + sin(1)^2*cos(2)*sin(2)/24
Numerical answer [src] 
0.359952401345828
0.359952401345828

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

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