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Solving integrals/ (sin^2)x(cos^3)xdx

Integral of (sin^2)x(cos^3)xdx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  sin (x)*x*cos (x)*x dx
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$$\int\limits_{0}^{1} x x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}\, dx$$ 
Integral(((sin(x)^2*x)*cos(x)^3)*x, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                                                                                                 
 |                                     5             2       3            4                2    5              5       2    2       3             4                     3       2   
 |    2         3               856*sin (x)   338*cos (x)*sin (x)   52*cos (x)*sin(x)   2*x *sin (x)   52*x*cos (x)   x *cos (x)*sin (x)   4*x*sin (x)*cos(x)   26*x*cos (x)*sin (x)
 | sin (x)*x*cos (x)*x dx = C - ----------- - ------------------- - ----------------- + ------------ + ------------ + ------------------ + ------------------ + --------------------
 |                                  3375              675                  225               15            225                3                    15                    45         
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$$\int x x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}\, dx = C + \frac{2 x^{2} \sin^{5}{\left(x \right)}}{15} + \frac{x^{2} \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{3} + \frac{4 x \sin^{4}{\left(x \right)} \cos{\left(x \right)}}{15} + \frac{26 x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{45} + \frac{52 x \cos^{5}{\left(x \right)}}{225} - \frac{856 \sin^{5}{\left(x \right)}}{3375} - \frac{338 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{675} - \frac{52 \sin{\left(x \right)} \cos^{4}{\left(x \right)}}{225}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         5            5             2       3            4                  4                   3       2   
  406*sin (1)   52*cos (1)   113*cos (1)*sin (1)   52*cos (1)*sin(1)   4*sin (1)*cos(1)   26*cos (1)*sin (1)
- ----------- + ---------- - ------------------- - ----------------- + ---------------- + ------------------
      3375         225               675                  225                 15                  45
$$- \frac{406 \sin^{5}{\left(1 \right)}}{3375} - \frac{113 \sin^{3}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{675} - \frac{52 \sin{\left(1 \right)} \cos^{4}{\left(1 \right)}}{225} + \frac{52 \cos^{5}{\left(1 \right)}}{225} + \frac{26 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{45} + \frac{4 \sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{15}$$ 
=
= 
         5            5             2       3            4                  4                   3       2   
  406*sin (1)   52*cos (1)   113*cos (1)*sin (1)   52*cos (1)*sin(1)   4*sin (1)*cos(1)   26*cos (1)*sin (1)
- ----------- + ---------- - ------------------- - ----------------- + ---------------- + ------------------
      3375         225               675                  225                 15                  45
$$- \frac{406 \sin^{5}{\left(1 \right)}}{3375} - \frac{113 \sin^{3}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{675} - \frac{52 \sin{\left(1 \right)} \cos^{4}{\left(1 \right)}}{225} + \frac{52 \cos^{5}{\left(1 \right)}}{225} + \frac{26 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{45} + \frac{4 \sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{15}$$ 
-406*sin(1)^5/3375 + 52*cos(1)^5/225 - 113*cos(1)^2*sin(1)^3/675 - 52*cos(1)^4*sin(1)/225 + 4*sin(1)^4*cos(1)/15 + 26*cos(1)^3*sin(1)^2/45
Numerical answer [src] 
0.0509642505862088
0.0509642505862088

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

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