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Q. 12

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Calculus
Found in: Page 428
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Find three integrals in Exercises 27–70 for which a good strategy is to apply integration by parts twice.

x2cosxdx, x2e3xdx, e2xsinxdx

See the step by step solution

Step by Step Solution

Step 1. Given information

Integration by parts should be applied twice.

Step 2. Observing the integrals

  • The integral x2cosxdx is the product of two functions namely x2 and cosxdx. It can be solved by taking u=x2, localid="1648731171575" dv=cosxdx. However, even by using these substitutions, the integral is not solved properly which leads to the further integration of the obtained expression to obtain the simplified resultant.
  • The integral x2e3xdx is the product of two functions namely x2 and e3xdx. It can be solved by taking u=x2, dv=e3xdx. However, even by using these substitutions, the integral is not solved properly which leads to the further integration of the obtained expression to obtain the simplified resultant.
  • The integral e2xsinxdx is the product of two functions namely e2x and sinxdx. It can be solved by taking u=e2x, dv=sinxdx. However, even by using these substitutions, the integral is not solved properly which leads to the further integration of the obtained expression to obtain the simplified resultant.

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