Integration By Parts

[bguyott]

Integration By Parts Functionality
To be implemented in the Multiply class, as the integrand of all integrals where IBP is appropriate include multiplication.

Requirements:

• Must determine which parts of the integrand and differential should be “u” or “dv” according to the rules of LIPET (assigning “u”):

• Logarithms

• Inverse Trigonometry

• Polynomials

• Exponential

• Trigonometry

• Integrate “dv” and differentiate “u”.

• Perform the substitution: ∫ udv = uv - ∫ vdu

• Check to determine whether ∫ vdu is able to be integrated through existing integration techniques. If not, then perform integration by parts again.

• Implement error-checking to ensure a ∫ vdu result that cannot be integrated does not get stuck in an infinite integration loop.

• Result is the simplified, integrated expression.

Expected date of completion: February 20, 2026