Exercise is mixed —some require integration by parts, while others can be integrated by using techniques discussed in the chapter on integration.
∫^2_1 (1-x^2)e^2x dx.

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Step-by-step explanation:

We have been given the indefinite integral . We are asked to find the integral using integration by parts.

We will use Integration by parts formula to solve our given problem.

Let and .

Now, we need to find du and v using these values as shown below:

Upon substituting these values in integration by parts formula, we will get:

Let us compute the boundaries.

Therefore, the value pf the given definite integral would be .