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Chapter 5: Q. 54 (page 429)

Solve each of the integrals in Exercises 27鈥�70. Some integrals require integration by parts, and some do not. (The last two exercises involve hyperbolic functions.)

鈭�x2x-1dx

Short Answer

Expert verified

The value is2(x-1)55+4(x-1)33+2(x-1)+C

Step by step solution

01

Step 1. Given information.

The given integral is鈭�x2x-1dx.

02

Step 2. Value of the integral.

Now, let

u=x-1du=12x-1dx鈭�x2x-1dx=鈭�2u2+12du2鈭�u4du+2鈭�u2du+鈭�1du=2u55+2u33+u+C=2(x-1)55+4(x-1)33+2(x-1)+C

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Most popular questions from this chapter

Suppose u(x)=x2. Calculate and compare the values of the following definite integrals:

role="math" localid="1648786835678" 鈭�-15u2du,鈭�x=-1x=5u2duand鈭�u(-1)u(5)u2du

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

u(x)=x2+x+1

For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.

鈭�u2du

Consider the integral 鈭�sinxcosxdx.

(a) Solve this integral by using u-substitution with u=sinx and du=cosxdx.

(b) Solve the integral another way, using u-substitution with u=cosx and du=鈭�sinxdx.

(c) How must your two answers be related? Use algebra to prove this relationship.

Write sin(2cos-1x)as an algebraic function.
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