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How can you compute the domain of g and g'(t) without computing any integrals in its definiton?

g(t)= ∫0t((1/1-x)+(1/(1+x)^2))dx  

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Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
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By the Fundamental Theorem of Calculus, g'(t) = 1/(1-t) + 1/(1+t)2.
 
   Domain g'(t) = {t l 1-t≠0 and 1+t≠0}
 
                      = {t l t ≠ ±1}