Mister Exam

Other calculators

  • How to use it?

  • Integral of d{x}:
  • Integral of sec^3(x) Integral of sec^3(x)
  • Integral of e^y Integral of e^y
  • Integral of |x|
  • Integral of xe^(x^2) Integral of xe^(x^2)

  • Identical expressions

  • x^ three *cos^ three (x)
  • x cubed multiply by co sinus of e of cubed (x)
  • x to the power of three multiply by co sinus of e of to the power of three (x)
  • x3*cos3(x)
  • x3*cos3x
  • x³*cos³(x)
  • x to the power of 3*cos to the power of 3(x)
  • x^3cos^3(x)
  • x3cos3(x)
  • x3cos3x
  • x^3cos^3x
  • x^3*cos^3(x)dx
Solving integrals/ x^3*cos^3(x)

Integral of x^3*cos^3(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |   3    3      
 |  x *cos (x) dx
 |               
/                
-1
$$\int\limits_{-1}^{1} x^{3} \cos^{3}{\left(x \right)}\, dx$$ 
Integral(x^3*cos(x)^3, (x, -1, 1))
The answer (Indefinite) [src] 
  /                                                                                                                                                                
 |                            3              3            2                3    3         2    3                                                        2          
 |  3    3             122*cos (x)   40*x*sin (x)   40*sin (x)*cos(x)   2*x *sin (x)   7*x *cos (x)    3    2                2    2             14*x*cos (x)*sin(x)
 | x *cos (x) dx = C - ----------- - ------------ - ----------------- + ------------ + ------------ + x *cos (x)*sin(x) + 2*x *sin (x)*cos(x) - -------------------
 |                          27            9                 9                3              3                                                            3         
/
$$\int x^{3} \cos^{3}{\left(x \right)}\, dx = C + \frac{2 x^{3} \sin^{3}{\left(x \right)}}{3} + x^{3} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 2 x^{2} \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{7 x^{2} \cos^{3}{\left(x \right)}}{3} - \frac{40 x \sin^{3}{\left(x \right)}}{9} - \frac{14 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3} - \frac{40 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{9} - \frac{122 \cos^{3}{\left(x \right)}}{27}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
0
$$0$$ 
=
= 
0
$$0$$ 
0
Numerical answer [src] 
0.0
0.0

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

    © Mister Exam – Calculator