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x^2sin^3x
Solving integrals/ x^2sin^3x

Integral of x^2sin^3x dx

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The solution

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∫01x2sin⁡3(x) dx\int\limits_{0}^{1} x^{2} \sin^{3}{\left(x \right)}\, dx 
Integral(x^2*sin(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                                         
 |                           3         2    3              3            2                                        2          
 |  2    3             40*cos (x)   2*x *cos (x)   14*x*sin (x)   14*sin (x)*cos(x)    2    2             4*x*cos (x)*sin(x)
 | x *sin (x) dx = C + ---------- - ------------ + ------------ + ----------------- - x *sin (x)*cos(x) + ------------------
 |                         27            3              9                 9                                       3         
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∫x2sin⁡3(x) dx=C−x2sin⁡2(x)cos⁡(x)−2x2cos⁡3(x)3+14xsin⁡3(x)9+4xsin⁡(x)cos⁡2(x)3+14sin⁡2(x)cos⁡(x)9+40cos⁡3(x)27\int x^{2} \sin^{3}{\left(x \right)}\, dx = C - x^{2} \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{2 x^{2} \cos^{3}{\left(x \right)}}{3} + \frac{14 x \sin^{3}{\left(x \right)}}{9} + \frac{4 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3} + \frac{14 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{9} + \frac{40 \cos^{3}{\left(x \right)}}{27}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
             3            3           2                  2          
  40   14*sin (1)   22*cos (1)   4*cos (1)*sin(1)   5*sin (1)*cos(1)
- -- + ---------- + ---------- + ---------------- + ----------------
  27       9            27              3                  9
−4027+22cos⁡3(1)27+5sin⁡2(1)cos⁡(1)9+4sin⁡(1)cos⁡2(1)3+14sin⁡3(1)9- \frac{40}{27} + \frac{22 \cos^{3}{\left(1 \right)}}{27} + \frac{5 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{9} + \frac{4 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \sin^{3}{\left(1 \right)}}{9} 
=
= 
             3            3           2                  2          
  40   14*sin (1)   22*cos (1)   4*cos (1)*sin(1)   5*sin (1)*cos(1)
- -- + ---------- + ---------- + ---------------- + ----------------
  27       9            27              3                  9
−4027+22cos⁡3(1)27+5sin⁡2(1)cos⁡(1)9+4sin⁡(1)cos⁡2(1)3+14sin⁡3(1)9- \frac{40}{27} + \frac{22 \cos^{3}{\left(1 \right)}}{27} + \frac{5 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{9} + \frac{4 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \sin^{3}{\left(1 \right)}}{9} 
-40/27 + 14*sin(1)^3/9 + 22*cos(1)^3/27 + 4*cos(1)^2*sin(1)/3 + 5*sin(1)^2*cos(1)/9
Numerical answer [src] 
0.113945544348484
0.113945544348484
The graph
Integral of x^2sin^3x dx

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

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