00:01
To integrate the integral of x -cube times e to the x dx, we apply integration by parts.
00:07
Now, integration by parts states that the integral of udv, this is equal to uv minus the integral of v, du.
00:16
And so for this integral, we let u be the algebraic expression x -cube, and we set dv equal to the remaining expression e -to -the -x -d -d -x.
00:29
Now if u is x cube, then the differential of u would be 3x squared dx, and integrating dv, we have v equal to e to the x.
00:43
And so by integration by parts, the integral of x cubed times e to the x d x, this is equal to uv minus the integral of v -d -u, or thus just x -cube times e to the x -d -mines the integral of v -du, or thus just x -cube times e to the x minus the integral of 3x squared dx times e to the x which will be x cube times e to the x minus 3 times the integral of x squared times e to the x d x now we need to apply integration part by parts again for the integral x squared times e to the x d x in here we let you be x squared and dv will be the same, e to the x, dx...