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xsin^2(x)x
Solving integrals/ xsin^2(x)x

Integral of xsin^2(x)x dx

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The solution

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∫01xxsin⁡2(x) dx\int\limits_{0}^{1} x x \sin^{2}{\left(x \right)}\, dx 
Integral((x*sin(x)^2)*x, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                       
 |                           2           2                       3    2       3    2       2              
 |      2               x*cos (x)   x*sin (x)   cos(x)*sin(x)   x *cos (x)   x *sin (x)   x *cos(x)*sin(x)
 | x*sin (x)*x dx = C - --------- + --------- + ------------- + ---------- + ---------- - ----------------
 |                          4           4             4             6            6               2        
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∫xxsin⁡2(x) dx=C+x3sin⁡2(x)6+x3cos⁡2(x)6−x2sin⁡(x)cos⁡(x)2+xsin⁡2(x)4−xcos⁡2(x)4+sin⁡(x)cos⁡(x)4\int x x \sin^{2}{\left(x \right)}\, dx = C + \frac{x^{3} \sin^{2}{\left(x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(x \right)}}{6} - \frac{x^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{x \sin^{2}{\left(x \right)}}{4} - \frac{x \cos^{2}{\left(x \right)}}{4} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
     2           2                   
  cos (1)   5*sin (1)   cos(1)*sin(1)
- ------- + --------- - -------------
     12         12            4
−sin⁡(1)cos⁡(1)4−cos⁡2(1)12+5sin⁡2(1)12- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{4} - \frac{\cos^{2}{\left(1 \right)}}{12} + \frac{5 \sin^{2}{\left(1 \right)}}{12} 
=
= 
     2           2                   
  cos (1)   5*sin (1)   cos(1)*sin(1)
- ------- + --------- - -------------
     12         12            4
−sin⁡(1)cos⁡(1)4−cos⁡2(1)12+5sin⁡2(1)12- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{4} - \frac{\cos^{2}{\left(1 \right)}}{12} + \frac{5 \sin^{2}{\left(1 \right)}}{12} 
-cos(1)^2/12 + 5*sin(1)^2/12 - cos(1)*sin(1)/4
Numerical answer [src] 
0.157041197450242
0.157041197450242
The graph
Integral of xsin^2(x)x dx

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

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