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Find three integrals in Exercises 27–70 for which either algebra or u-substitution is a better strategy than integration by parts.

Short Answer

Expert verified

xsinx2dx, 3xex2dx,3x+1xdx

Step by step solution

01

Step 1. Given information

Integrals should be easily solved by u- substitution or algebra instead of integration by parts.

02

Step 2. Observing integrals

  • The integral xsinx2dxcan easily be solved by using u- substitution as for u=x2, the derivative du of u equals 2xdx. Hence, the transformed integral 12sinuducan be solved simply.
  • The integral 3xex2dxcan easily be solved by using u- substitution as for u=x2, the derivative du of u equals 2xdx. Hence, the transformed integral 3eu2ducan be solved simply.
  • The integral 3x+1xdxcan easily be solved by using algebra because the integrand can be simplified as3+1x. Hence, the transformed integral 3+1xdxcan be solved simply.

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