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Integration by parts formula

∫udv= uv-∫vdu

The integration by parts formula is a technique used in calculus to integrate the product of two functions. It states that for two functions f(x) and g(x), the integral of their product, fg(x), can be expressed as follows:

∫f(x)g(x)dx = f(x)∫g(x)dx – ∫[f'(x)∫g(x)dx]dx

where f'(x) is the derivative of f(x) with respect to x.

This formula involves breaking down the integrand into two parts, f(x) and g(x), one of which is easily integrated and the other is differentiated. By applying this formula, we can simplify complex integrals and make them easier to solve.

It is important to choose the functions f(x) and g(x) carefully, as this can affect the outcome of the integral. A common technique is to choose f(x) to be a function whose derivative becomes simpler or zero after differentiation, and g(x) to be a function whose integral is easy to compute. The choice of functions will depend on the specific problem at hand.

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