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Some Tricks Exercises

Example 1

Apply the formula for integration by parts with u = ln x and v' = 1 to find

Example 2

Use integration by parts to find .

Example 3

Find

by applying the formula for integration by parts with u = x3 and v' = x2ex3.

Example 4

Find

Example 5

Use integration by parts to find

taking u = sin x for the first integration.

Example 6

Integrate.

Example 7

Integrate.

Example 8

Integrate.

Example 9

Integrate.

Example 10

Integrate.

Example 11

Integrate.

Example 12

Integrate.