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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo                    
  /                    
 |                     
 |   x*(-3)            
 |  2      *sin(2*x) dx
 |                     
/                      
0                      
$$\int\limits_{0}^{\infty} 2^{\left(-3\right) x} \sin{\left(2 x \right)}\, dx$$
Integral(2^(x*(-3))*sin(2*x), (x, 0, oo))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                                                     
 |                                       2                         2                                    
 |  x*(-3)                          2*cos (x)                 2*sin (x)           6*cos(x)*log(2)*sin(x)
 | 2      *sin(2*x) dx = C - ----------------------- + ----------------------- - -----------------------
 |                              3*x      3*x    2         3*x      3*x    2         3*x      3*x    2   
/                            4*2    + 9*2   *log (2)   4*2    + 9*2   *log (2)   4*2    + 9*2   *log (2)
$$\int 2^{\left(-3\right) x} \sin{\left(2 x \right)}\, dx = C + \frac{2 \sin^{2}{\left(x \right)}}{4 \cdot 2^{3 x} + 9 \cdot 2^{3 x} \log{\left(2 \right)}^{2}} - \frac{6 \log{\left(2 \right)} \sin{\left(x \right)} \cos{\left(x \right)}}{4 \cdot 2^{3 x} + 9 \cdot 2^{3 x} \log{\left(2 \right)}^{2}} - \frac{2 \cos^{2}{\left(x \right)}}{4 \cdot 2^{3 x} + 9 \cdot 2^{3 x} \log{\left(2 \right)}^{2}}$$
The graph
The answer [src]
      2      
-------------
         2   
4 + 9*log (2)
$$\frac{2}{4 + 9 \log{\left(2 \right)}^{2}}$$
=
=
      2      
-------------
         2   
4 + 9*log (2)
$$\frac{2}{4 + 9 \log{\left(2 \right)}^{2}}$$
2/(4 + 9*log(2)^2)

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