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Chapter 5: Q. 51 (page 442)

Calculate each of the definite integrals in Exercises 47鈥�52. Some integrals require partial fractions or polynomial long division, and some do not.

鈭�-11x2-2x-4x-3dx

Short Answer

Expert verified

The value is2-ln(2)

Step by step solution

01

Step 1. Given Information: 

Given definite integral :鈭�-11x2-2x-4x-3dx

We want to calculate each of the definite integrals.

02

Step 2. Calculation: 

Use long divisor method we get

x2-2x-4x-3=x+1-1x-3Now鈭�-11x2-2x-4x-3dx=鈭�-11xdx+鈭�-111dx-鈭�-111x-3dx=x22-11+x-11-ln|x-3|-11=12-12+[1-(-1)]-(ln|-2|-ln|-4|)=0+2-ln(2)=2-ln(2)

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Most popular questions from this chapter

Consider the integral 鈭�x(x2鈭�1)2dx.

(a) Solve this integral by using u-substitution.

(b) Solve the integral another way, using algebra to multiply out the integrand first.

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

Find three integrals in Exercises 21鈥�70 in which the denominator of the integrand is a good choice for a substitution u(x).

Solve the integral

鈭�3-xx-1dx

Solve the integral:鈭�lnxdx

Solve鈭�x21+x2dx the following two ways:

(a) with the substitution u=tan-1x;

(b) with the trigonometric substitution x = tan u.
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