Let I = ∫x2ex dx
Taking \(x^2\) as first function and ex as second function and integrating by parts, we obtain
I= x2∫ex dx - ∫{\((\frac {d}{dx}x^2)\)∫exdx} dx
I = x2ex - ∫2x.exdx
I = x2ex-2∫x.ex dx
Again integrating by parts,we obtain
I =x2ex - 2[x.∫exdx - ∫{\((\frac {d}{dx}x)\).∫exdx} dx]
I = x2ex - 2[xex-∫exdx]
I = x2ex - 2[xex - ex]
I = x2ex - 2xex + 2ex + C
I = ex(x2 - 2x + 2) + C
What is the Planning Process?
The number of formulas used to decompose the given improper rational functions is given below. By using the given expressions, we can quickly write the integrand as a sum of proper rational functions.
For examples,