Integration by Parts Formulas
We can derive the integration of various functions using the integration by parts concept. Some of the important formulas derived using this technique are
- ∫ ex(f(x) + f'(x)).dx = exf(x) + C
- ∫√(x2 + a2).dx = ½ . x.√(x2 + a2)+ a2/2. log|x + √(x2 + a2)| + C
- ∫√(x2 – a2).dx =½ . x.√(x2 – a2) – a2/2. log|x +√(x2 – a2) | C
- ∫√(a2 – x2).dx = ½ . x.√(a2 – x2) + a2/2. sin-1 x/a + C
Integration by Parts
Integration by Parts: Integration by parts is a technique used in calculus to find the integral of the product of two functions. It’s essentially a reversal of the product rule for differentiation.
Integrating a function is not always easy sometimes we have to integrate a function that is the multiple of two or more functions in this case if we have to find the integration we have to use integration by part concept, which uses two products of two functions and tells us how to find their integration.
Now let’s learn about Integration by parts, its formula, derivation, and others in detail in this article.
Table of Content
- What is Integration by Parts?
- What is Partial Integration?
- Integration By Parts Formula
- Derivation of Integration By Parts Formula
- ILATE Rule
- How to Find Integration by Part?
- Repeated Integration by Parts
- Applications of Integration by Parts
- Integration by Parts Formulas
- Integration By Parts Examples
- Practice Problems
- FAQs
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