oo / | | x*(-3) | 2 *sin(2*x) dx | / 0
Integral(2^(x*(-3))*sin(2*x), (x, 0, oo))
The integral of a constant times a function is the constant times the integral of the function:
Don't know the steps in finding this integral.
But the integral is
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | 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)
2 ------------- 2 4 + 9*log (2)
=
2 ------------- 2 4 + 9*log (2)
2/(4 + 9*log(2)^2)
Use the examples entering the upper and lower limits of integration.