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Chapter 5: Q. 10 (page 428)

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

Short Answer

Expert verified

鈭�xsinx2dx, 鈭�3xex2dx,鈭�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 鈭�xsinx2dxcan easily be solved by using u- substitution as for u=x2, the derivative du of u equals 2xdx. Hence, the transformed integral 12鈭�sinuducan be solved simply.
  • The integral 鈭�3xex2dxcan easily be solved by using u- substitution as for u=x2, the derivative du of u equals 2xdx. Hence, the transformed integral 3鈭�eu2ducan be solved simply.
  • The integral 鈭�3x+1xdxcan easily be solved by using algebra because the integrand can be simplified as3+1x. Hence, the transformed integral 鈭�3+1xdxcan be solved simply.

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Most popular questions from this chapter

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

鈭�xx2+1dx

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

鈭�4-x2x2dx

For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.

u(x)=x2+1

Solve the integral:鈭�lnxdx

Suppose v(x) is a function of x. Explain why the integral

of dv is equal to v (up to a constant).
See all solutions

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