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Solving integrals/ x*sin(3x^2)

Integral of x*sin(3x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       /   2\   
 |  x*sin\3*x / dx
 |                
/                 
0
$$\int\limits_{0}^{1} x \sin{\left(3 x^{2} \right)}\, dx$$ 
Integral(x*sin(3*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 sine is negative cosine:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                              
 |                         /   2\
 |      /   2\          cos\3*x /
 | x*sin\3*x / dx = C - ---------
 |                          6    
/
$$\int x \sin{\left(3 x^{2} \right)}\, dx = C - \frac{\cos{\left(3 x^{2} \right)}}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1   cos(3)
- - ------
6     6
$$\frac{1}{6} - \frac{\cos{\left(3 \right)}}{6}$$ 
=
= 
1   cos(3)
- - ------
6     6
$$\frac{1}{6} - \frac{\cos{\left(3 \right)}}{6}$$ 
1/6 - cos(3)/6
Numerical answer [src] 
0.331665416100074
0.331665416100074

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

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