1 / | | -x | x*e dx | / 0
Integral(x*exp(-x), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
Use integration by parts:
Let and let .
Then .
To find :
The integral of the exponential function is itself.
Now evaluate the sub-integral.
The integral of the exponential function is itself.
Now substitute back in:
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:
/ | | -x -x -x | x*e dx = C - e - x*e | /
Use the examples entering the upper and lower limits of integration.