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

Short Answer

Expert verified

x2cosxdx,x2e3xdx,e2xsinxdx

Step by step solution

01

Step 1. Given information

Integration by parts should be applied twice.

02

Step 2. Observing the integrals

  • The integral x2cosxdxis the product of two functions namely x2and 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 x2e3xdxis the product of two functions namely x2and 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 e2xsinxdxis the product of two functions namely e2xand 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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