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Chapter 4: Q. 38 (page 362)

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess-and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating.

鈭�x-11-x-1dx

Short Answer

Expert verified

The solution of the integral is lnx-1+C.

Step by step solution

01

Step 1. Given Information. 

The given integral is鈭�x-11-x-1dx.

02

Step 2. Solve. 

By solving the integral we get,

鈭�x-11-x-1dx=鈭�1x1-1xdx=鈭�1x1-1xdx=鈭�1x-1dx=lnx-1+C

03

Step 3. Verification. 

To verify the answer we differentiate lnx-1+Cit.

On differentiating we get,

lnx-1+C=ddxlnx-1+ddxC=1x-1+0=1x-1=x-11-x-1

Hence proved.

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