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Finding the anti-derivative.
 

A challenging anti-derivative

Find the following antiderivative:



Problem Moderated by: MrT

  
 
 
 

Problem Solution

Since we can't factor the denominator, we can't integrate by partial fractions in the form it currently is in. However, we can algebraically divide the integrand to get the following: x - x/(1 + x2). The integral of the first part is x2/2, while the integral of the second is simply (1/2)ln(1 + x2). The final result is then:

x2/2 - (1/2)ln(1 + x2) + C.

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