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

344x2-4dx

Short Answer

Expert verified

The value is-ln(3)+ln(5)

Step by step solution

01

Step 1. Given Information:

Given definite integral 344x2-4dx

We want to calculate each of the definite integrals.

02

Step 2. Calculation:

We have

344x2-4dx=4341x2-4dxSubstitutionx=2uWhenx=4thenu=2andwhenx=3thenu=32andalsodx=2duApplyIntegralSubstitution:432214(u2-1)2du=23221(u2-1)du=23221-(-u2+1)du=-232211-u2du=-2lnu+12-lnu-12232=-lnu+1-lnu-1232=-ln|3|-ln|1|-ln|52|-ln|12|Uselogproperties:=ln(3)-ln(52)-ln(2)=-ln(3)+ln(5)

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