1 / | | / 2\ | 3 \x / | x *E dx | / 0
Integral(x^3*E^(x^2), (x, 0, 1))
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
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.
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | / 2\ / 2\ | / 2\ \x / 2 \x / | 3 \x / e x *e | x *E dx = C - ----- + -------- | 2 2 /
Use the examples entering the upper and lower limits of integration.