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xcos(3-4x^2)dx
Solving integrals/ xcos(3-4x^2)dx

Integral of xcos(3-4x^2)dx dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |       /       2\   
 |  x*cos\3 - 4*x / dx
 |                    
/                     
0
$$\int\limits_{0}^{1} x \cos{\left(3 - 4 x^{2} \right)}\, dx$$ 
Integral(x*cos(3 - 4*x^2), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                       
 |                             /        2\
 |      /       2\          sin\-3 + 4*x /
 | x*cos\3 - 4*x / dx = C + --------------
 |                                8       
/
$$\int x \cos{\left(3 - 4 x^{2} \right)}\, dx = C + \frac{\sin{\left(4 x^{2} - 3 \right)}}{8}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
sin(1)   sin(3)
------ + ------
  8        8
$$\frac{\sin{\left(3 \right)}}{8} + \frac{\sin{\left(1 \right)}}{8}$$ 
=
= 
sin(1)   sin(3)
------ + ------
  8        8
$$\frac{\sin{\left(3 \right)}}{8} + \frac{\sin{\left(1 \right)}}{8}$$ 
sin(1)/8 + sin(3)/8
Numerical answer [src] 
0.12282387410847
0.12282387410847
The graph
Integral of xcos(3-4x^2)dx dx

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

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