oo / | | -t | --- | 2 | t*e dt | / 0
Integral(t*exp((-t)/2), (t, 0, oo))
Use integration by parts:
Let and let .
Then .
To find :
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of the exponential function is itself.
So, the result is:
Now substitute back in:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of the exponential function is itself.
So, the result is:
Now substitute back in:
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | -t -t -t | --- --- --- | 2 2 2 | t*e dt = C - 4*e - 2*t*e | /
Use the examples entering the upper and lower limits of integration.