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What is the formula for integration by parts?

Integration by parts or partial integration is a theorem that relates the integral of a product of functions to the integral of their derivative and antiderivative. The Integration by parts formula is : \[\large \int u\;v\;dx=u\int v\;dx-\int\left(\frac{du}{dx}\int v\;dx\right)dx\] Where $u$ and $v$ are the differentiable functions of $x$.

What is the importance of integration by parts?

Integration by parts is a technique for performing indefinite integration or definite integration by expanding the differential of a product of functions and expressing the original integral in terms of a known integral .


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