/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 49 Calculate each of the definite i... [FREE SOLUTION] | 91影视

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Chapter 5: Q. 49 (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�131x(x+1)dx

Short Answer

Expert verified

The value isln(3)-ln(2)

Step by step solution

01

Step 1. Given Information: 

Given definite integral :鈭�131x(x+1)dx

We want to calculate each of the definite integrals.

02

Step 2. Calculation: 

Use partial fraction we get:

1x(x+1)=Ax+Bx+11=A(x+1)+BxComparethecoefficientweget1=Aand0=A+B1=Aand-1=BUsethesevaluesweget:1x(x+1)=1x-1x+1Now鈭�131x(x+1)dx=鈭�131xdx-鈭�131x+1dx=ln|x|13-ln|x+1|13=ln(3)-ln(1)-(ln(4)-ln(2))Usinglogproperties:=ln(3)-ln(2)

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