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Chapter 5: Q. 74 (page 465)

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�xsin-1xdx

Short Answer

Expert verified

The value of integral is-133e-x2+1+C

Step by step solution

01

Step 1. Given information

An expression is given as鈭�xsin-1xdx

02

Step 2. Solving Integral

Let

u=sin-1xdu=dx-x2+1v=鈭�xdx=x

Now substitute the values and simplify as,

鈭�xsin-1xdx=sin-1xx22-鈭�x22路1-x2+1dx=-鈭�u3u2+1du=-鈭�16vdv=-16鈭�1vdv=-133u2+1+C=-133e-x2+1+C

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Most popular questions from this chapter

Solve the integral:鈭�xlnxdx

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

Which of the integrals that follow would be good candidates for trigonometric substitution? If a trigonometric substitution is a good strategy, name the substitution. If another method is a better strategy, explain that method.

(a)鈭�4+x2xdx (b)鈭�x4+x2dx

role="math" localid="1648759296940" (c)鈭�x24+x2dx (d)鈭�16鈭�x44+x2dx

Solve the integral:鈭�x2+1exdx

Complete the square for each quadratic in Exercises 28鈥�33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.

2(x+2)2
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