# How does integration by parts work?

Now, by Integration by Parts, #int xe^xdx =xe^x-inte^xdx=xe^x-e^x+C#

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Integration by parts is a technique used to evaluate integrals of the form ∫u dv. It is based on the product rule for differentiation, which states that the derivative of a product of two functions is equal to the derivative of the first function times the second function plus the first function times the derivative of the second function. The formula for integration by parts is:

∫u dv = uv - ∫v du

Where u and v are differentiable functions of x. To use integration by parts, you choose u and dv such that you can easily integrate dv or differentiate u. Then, you find du and v by differentiating u and integrating dv, respectively. Finally, you substitute these values into the integration by parts formula and evaluate the resulting integral.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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