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x^2cosx^3dx
Solving integrals/ x^2cosx^3dx

Integral of x^2cosx^3dx dx

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The solution

You have entered [src] 
  1              
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 |   2    3      
 |  x *cos (x) dx
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0
$$\int\limits_{0}^{1} x^{2} \cos^{3}{\left(x \right)}\, dx$$ 
Integral(x^2*cos(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                                         
 |                           3            2                2    3              3                                 2          
 |  2    3             40*sin (x)   14*cos (x)*sin(x)   2*x *sin (x)   14*x*cos (x)    2    2             4*x*sin (x)*cos(x)
 | x *cos (x) dx = C - ---------- - ----------------- + ------------ + ------------ + x *cos (x)*sin(x) + ------------------
 |                         27               9                3              9                                     3         
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$$\int x^{2} \cos^{3}{\left(x \right)}\, dx = C + \frac{2 x^{2} \sin^{3}{\left(x \right)}}{3} + x^{2} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{4 x \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{3} + \frac{14 x \cos^{3}{\left(x \right)}}{9} - \frac{40 \sin^{3}{\left(x \right)}}{27} - \frac{14 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{9}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        3            3           2                  2          
  22*sin (1)   14*cos (1)   5*cos (1)*sin(1)   4*sin (1)*cos(1)
- ---------- + ---------- - ---------------- + ----------------
      27           9               9                  3
$$- \frac{22 \sin^{3}{\left(1 \right)}}{27} - \frac{5 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{9} + \frac{14 \cos^{3}{\left(1 \right)}}{9} + \frac{4 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{3}$$ 
=
= 
        3            3           2                  2          
  22*sin (1)   14*cos (1)   5*cos (1)*sin(1)   4*sin (1)*cos(1)
- ---------- + ---------- - ---------------- + ----------------
      27           9               9                  3
$$- \frac{22 \sin^{3}{\left(1 \right)}}{27} - \frac{5 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{9} + \frac{14 \cos^{3}{\left(1 \right)}}{9} + \frac{4 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{3}$$ 
-22*sin(1)^3/27 + 14*cos(1)^3/9 - 5*cos(1)^2*sin(1)/9 + 4*sin(1)^2*cos(1)/3
Numerical answer [src] 
0.133497304240883
0.133497304240883
The graph
Integral of x^2cosx^3dx dx

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

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