Integration by Parts

Understanding Integration by Parts 🧮

Integration by parts is a powerful technique used to find integrals of products of functions. It is based on the product rule for differentiation and is often used in calculus when simpler integration methods do not suffice.

The formula for integration by parts is given by:

Where:

• u is a function of x
• dv is a differential of another function of x
• v is the integral of dv
• du is the differential of u

Examples and Applications ✨

To better understand how to use integration by parts, let's look at a simple example:

Suppose we want to integrate xe^x. We set:

• u = x → du = dx
• dv = e^x dx → v = e^x

Applying the formula:

∫xe^x dx = xe^x - ∫e^x dx = xe^x - e^x + C

Practice Makes Perfect! 🎯

The best way to master integration by parts is through practice. Try solving problems and applying this technique to different functions.