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Integration by Parts

(1) S xe^xdx

(2) S xsinxdx

(3) S lnxdx

(4) S (e^x)cosxdx

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INTEGRATION BY PARTS

The formula for integration by parts is:
(see attachment)

The hard part is knowing when to use this formula and how to choose appropriate u and dv.

Here are some examples of problems that you can solve using the method of integration by parts, and explanations on how to solve them.

(1) ∫xexdx

Let u = x and dv = exdx. That means du = 1dx and v = ex.

Plug those values for u, v, du, and dv into the integration by parts formula:

∫xexdx = (x)(ex) - ∫(ex)(dx)

Solve the integral:

∫xexdx = xex - ex + c

Now, what if we had let u = ex and dv = xdx? Then du = exdx and v = ...

Solution Summary

This posting has 4 examples of problems solved using the method of integration by parts. These involve integrating functions that include the terms e^x, ln(x), sin(x), and cos(x). The solution includes the formula for integration by parts as well as step-by-step explanations.

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