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Chapter 5: Q. 44 (page 417)

Solve each of the integrals in Exercises 21鈥�70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)

鈭�exxdx

Short Answer

Expert verified

The solution of the given integral is 鈭�exxdx=ex+C.

Step by step solution

01

Step 1. Given Information 

Solving the given integrals.

鈭�exxdx

02

Step 2. Solving the given integral using substitution method. 

u=xu=x1/2dudx=12x-1/2dudx=12x2du=1xdx

03

Step 3. This substitution changes the integral into 

鈭�exxdx=鈭�eudu鈭�exxdx=eu+C鈭�exxdx=ex+C

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Most popular questions from this chapter

Solve given definite integral.

鈭�04鈥�x3x2+4dx

Solve the integral:鈭�3-xe2xdx

Solve the integral:鈭�3x+1xdx

True/False: Determinewhethereachofthestatementsthat follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: f(x)=x+1x-1is a proper rational function.

(b) True or False: Every improper rational function can be expressed as the sum of a polynomial and a proper rational function.

(c) True or False: After polynomial long division of p(x) by q(x), the remainder r(x) has a degree strictly less than the degree of q(x).

(d) True or False: Polynomial long division can be used to divide two polynomials of the same degree.

(e) True or False: If a rational function is improper, then polynomial long division must be applied before using the method of partial fractions.

(f) True or False: The partial-fraction decomposition of x2+1x2(x-3)is of the form Ax2+Bx-3

(g) True or False: The partial-fraction decomposition of x2+1x2(x-3)is of the form Bx+Cx2+Ax-3.

(h) True or False: Every quadratic function can be written in the formA(x-k)2+C

Why don鈥檛 we ever have cause to use the trigonometric substitution x=cosu?
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