1 / | | 3 -x | x *E dx | / 0
Integral(x^3*E^(-x), (x, 0, 1))
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.
Use integration by parts:
Let and let .
Then .
To find :
The integral of the exponential function is itself.
Now evaluate the sub-integral.
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 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 simplify:
Add the constant of integration:
The answer is:
/ | | 3 -x -x 3 -x -x 2 -x | x *E dx = C - 6*e - x *e - 6*x*e - 3*x *e | /
-1 6 - 16*e
=
-1 6 - 16*e
6 - 16*exp(-1)
Use the examples entering the upper and lower limits of integration.