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  • Identical expressions

  • three *sin^ three (x)*(- six *sin(x)*cos^ two (x))
  • 3 multiply by sinus of cubed (x) multiply by ( minus 6 multiply by sinus of (x) multiply by co sinus of e of squared (x))
  • three multiply by sinus of to the power of three (x) multiply by ( minus six multiply by sinus of (x) multiply by co sinus of e of to the power of two (x))
  • 3*sin3(x)*(-6*sin(x)*cos2(x))
  • 3*sin3x*-6*sinx*cos2x
  • 3*sin³(x)*(-6*sin(x)*cos²(x))
  • 3*sin to the power of 3(x)*(-6*sin(x)*cos to the power of 2(x))
  • 3sin^3(x)(-6sin(x)cos^2(x))
  • 3sin3(x)(-6sin(x)cos2(x))
  • 3sin3x-6sinxcos2x
  • 3sin^3x-6sinxcos^2x
  • 3*sin^3(x)*(-6*sin(x)*cos^2(x))dx

  • Similar expressions

  • 3*sin^3(x)*(6*sin(x)*cos^2(x))
  • 3*sin^3(x)*(-6*sinx*cos^2(x))
Solving integrals/ 3*sin^3(x)*(-6*sin(x)*cos^2(x))

Integral of 3*sin^3(x)*(-6*sin(x)*cos^2(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                               
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 2                                
  /                               
 |                                
 |       3                 2      
 |  3*sin (x)*-6*sin(x)*cos (x) dx
 |                                
/                                 
0
$$\int\limits_{0}^{\frac{\pi}{2}} - 6 \sin{\left(x \right)} \cos^{2}{\left(x \right)} 3 \sin^{3}{\left(x \right)}\, dx$$ 
Integral((3*sin(x)^3)*((-6*sin(x))*cos(x)^2), (x, 0, pi/2))
The answer (Indefinite) [src] 
  /                                                                                                                                                                      
 |                                                                 6             6           5                  5                     2       4              4       2   
 |      3                 2                  3       3      9*x*cos (x)   9*x*sin (x)   9*sin (x)*cos(x)   9*cos (x)*sin(x)   27*x*cos (x)*sin (x)   27*x*cos (x)*sin (x)
 | 3*sin (x)*-6*sin(x)*cos (x) dx = C + 3*cos (x)*sin (x) - ----------- - ----------- - ---------------- + ---------------- - -------------------- - --------------------
 |                                                               8             8               8                  8                    8                      8          
/
$$\int - 6 \sin{\left(x \right)} \cos^{2}{\left(x \right)} 3 \sin^{3}{\left(x \right)}\, dx = C - \frac{9 x \sin^{6}{\left(x \right)}}{8} - \frac{27 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{8} - \frac{27 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{8} - \frac{9 x \cos^{6}{\left(x \right)}}{8} - \frac{9 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{8} + 3 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)} + \frac{9 \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{8}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-9*pi
-----
  16
$$- \frac{9 \pi}{16}$$ 
=
= 
-9*pi
-----
  16
$$- \frac{9 \pi}{16}$$ 
-9*pi/16
Numerical answer [src] 
-1.76714586764426
-1.76714586764426

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