Integration by Parts
Intuition
Integration by parts will typically apply whenever there are two values of x.
Procedure
Basic Example
The task is to integrate the following:
Integration by parts is the product rule in reverse, expressed in simplified form as:
Our first task is to set u, du, v and dv
Trigonometric Example
The task is to integrate the following:
Integration by Parts in Python 3
With Sympy
aaa
With Scipy
kaa
import scipy.integrate as integrate
import scipy.special as special
result = integrate.quad(lambda x: special.jv(2.5,x), 0, 4.5)
resultExplanation
Integration by parts applies whenever the integral takes the following form:
The full formula for integration by parts is analagous to the product rule, as follows:
The above equation is often simplified to: