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Identical expressions
(4sinx^ two)^ two +(two sin(2x))^2
(4 sinus of x squared ) squared plus (2 sinus of (2x)) squared
(4 sinus of x to the power of two) to the power of two plus (two sinus of (2x)) squared
(4sinx2)2+(2sin(2x))2
4sinx22+2sin2x2
(4sinx²)²+(2sin(2x))²
(4sinx to the power of 2) to the power of 2+(2sin(2x)) to the power of 2
4sinx^2^2+2sin2x^2
(4sinx^2)^2+(2sin(2x))^2dx
Similar expressions
(4sinx^2)^2-(2sin(2x))^2

Solving integrals/ (4sinx^2)^2+(2sin(2x))^2

Integral of (4sinx^2)^2+(2sin(2x))^2 dx

The solution

You have entered [src]

 pi                                  
  /                                  
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 |  /           2                \   
 |  |/     2   \                2|   
 |  \\4*sin (x)/  + (2*sin(2*x)) / dx
 |                                   
/                                    
0

$$\int\limits_{0}^{\pi} \left(\left(4 \sin^{2}{\left(x \right)}\right)^{2} + \left(2 \sin{\left(2 x \right)}\right)^{2}\right)\, dx$$

Integral((4*sin(x)^2)^2 + (2*sin(2*x))^2, (x, 0, pi))

Detail solution

Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $6 x \sin^{4}{\left(x \right)} + 12 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} + 6 x \cos^{4}{\left(x \right)} - 10 \sin^{3}{\left(x \right)} \cos{\left(x \right)} - 6 \sin{\left(x \right)} \cos^{3}{\left(x \right)}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $2 x \sin^{2}{\left(2 x \right)} + 2 x \cos^{2}{\left(2 x \right)} - \sin{\left(2 x \right)} \cos{\left(2 x \right)}$
The result is: $6 x \sin^{4}{\left(x \right)} + 12 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} + 2 x \sin^{2}{\left(2 x \right)} + 6 x \cos^{4}{\left(x \right)} + 2 x \cos^{2}{\left(2 x \right)} - 10 \sin^{3}{\left(x \right)} \cos{\left(x \right)} - 6 \sin{\left(x \right)} \cos^{3}{\left(x \right)} - \sin{\left(2 x \right)} \cos{\left(2 x \right)}$
Now simplify:

$8 x - 4 \sin{\left(2 x \right)}$
Add the constant of integration:

$8 x - 4 \sin{\left(2 x \right)}+ \mathrm{constant}$

The answer is:

$8 x - 4 \sin{\left(2 x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                                                                                                                                   
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 | /           2                \                                                                                                                                                     
 | |/     2   \                2|                                    3                  3                    2               2               4             4              2       2   
 | \\4*sin (x)/  + (2*sin(2*x)) / dx = C - cos(2*x)*sin(2*x) - 10*sin (x)*cos(x) - 6*cos (x)*sin(x) + 2*x*cos (2*x) + 2*x*sin (2*x) + 6*x*cos (x) + 6*x*sin (x) + 12*x*cos (x)*sin (x)
 |                                                                                                                                                                                    
/

$$-{{\sin \left(4\,x\right)}\over{2}}+8\,\left({{{{\sin \left(4\,x \right)}\over{2}}+2\,x}\over{8}}-{{\sin \left(2\,x\right)}\over{2}}+ {{x}\over{2}}\right)+2\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

8*pi

$$8 \pi$$

8*pi

$$8 \pi$$

Simplify

Numerical answer [src]

25.1327412287183

25.1327412287183

The graph

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

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Identical expressions

Similar expressions

Integral of (4sinx^2)^2+(2sin(2x))^2 dx

Limits of integration:

The graph:

Piecewise:

The solution