Techniques of Integration - Integration by Splitting the Numerator

Techniques of Integration - Integration by Splitting the Numerator

\(\displaystyle\displaystyle \displaystyle\int{\frac{{{x}^{2}}+2}{{{x}^{2}}+2x+3}\mathrm{ }}\mathrm{d}x\)

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Answer:\(x-\ln|x^2+2x+3|+\frac1{\sqrt2}\tan^{-1}\left(\frac{x+1}{\sqrt2}\right)+C\)

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