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Chapter 5: Q. 46 (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�x2+9x32dx

Short Answer

Expert verified

The solution of the integral is23x32-18x+C.

Step by step solution

01

Step 1. Given Information.

The given integral is鈭�x2+9x32dx.

02

Step 2. Solve. 

Let's solve the integral,

鈭�x2+9x32dx=鈭�x+9x32dx=鈭�xdx+鈭�9x32dx=23x32+9-21x+C=23x32-18x+C

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Most popular questions from this chapter

Solve the integral:鈭�xcosxdx.

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

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

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

Why don鈥檛 we need to have a square root involved in order to apply trigonometric substitution with the tangent? In other words, why can we use the substitution x=atan鈦�uwhen we see x2+a2, even though we can鈥檛 use the substitution x=asin鈦�uunless the integrand involves the square root ofa2鈭�x2? (Hint: Think about domains.)

Solve given definite integral.

鈭�12鈥�39鈭�2x23/2dx
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