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CBSE Class 12 · 2006 · Indefinite IntegralsVery Short Answer

Evaluate :

\int \frac{x + 3}{x ^{2} + 4 x + 3} d x

Answer: $lo g ∣ x + 1∣ + C$

Solution

Factor the denominator:

x^{2} + 4 x + 3 = (x + 1) (x + 3)

. Therefore

\frac{x + 3}{( x + 1 ) ( x + 3 )} = \frac{1}{x + 1} .

Integrating the reduced fraction,

\int \frac{d x}{x + 1} = lo g ∣ x + 1∣ + C

CBSE Class 12 Board · 2006 · Subjective

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