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- Integration is a mathematical process that involves finding the antiderivative of a given function. Integration formulas are rules that help us to find the integral of various types of functions. There are many integration formulas, but some of the most common ones are:
- - The power rule: ∫ x^n dx = x^(n+1) / (n+1) + C, where n is any constant except -1 and C is an arbitrary constant .
- - The constant rule: ∫ c dx = cx + C, where c is any constant .
- - The logarithmic rule: ∫ 1/x dx = log|x| + C, where x is not zero .
- - The exponential rule: ∫ e^x dx = e^x + C .
- - The general exponential rule: ∫ a^x dx = a^x / loga + C, where a is any positive constant except 1 .
- - The integration by parts rule: ∫ f(x)g(x) dx = f(x)∫g(x) dx - ∫ (∫g(x) dx)f'(x) dx + C, where f and g are differentiable functions .
- These integration formulas can be used to find the integral of simple or complex functions by applying them directly or combining them with other techniques such as substitution, trigonometric identities, partial fractions, etc. Integration formulas are useful for solving problems involving area under curves, volume of solids of revolution, work done by forces, etc.[5]
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