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Solve each of the integrals in Exercises 7578by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.
x2-1x2+1dx

Short Answer

Expert verified

The value of integral isx-2tan-1(x)+C

Step by step solution

01

Step 1. Given informaion

An expression is given asx2-1x2+1dx

02

Step 2. Solving integral

Split the term by using long distance method and simplify as,

x2-1x2+1=1-2x2+11-2x2+1dx=1dx-21x2+1dx=x-2tan-1(x)+C

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