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प्रश्न
Evaluate \[\int\frac{x+2}{2x^2+6x+5}\,dx\].
पर्याय
\[\frac14\log|2x^2+6x+5|+\tan^{-1}(2x+3)+C\]
\[\frac14\log|2x^2+6x+5|+\frac12\tan^{-1}(2x+3)+C\]
\[\frac12\log|2x^2+6x+5|+\frac14\tan^{-1}(2x+3)+C\]
\[\frac14\log|2x^2+6x+5|+\frac12\sin^{-1}(2x+3)+C\]
MCQ
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उत्तर
The derivative-related part gives \[\frac14\log|2x^2+6x+5|\]. Completing the square in the remaining integral gives \[\tan^{-1}(2x+3)\], multiplied by \[\frac12\].
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