A Level

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Evaluate ∫2x+3x2+3x+2 dx\displaystyle\int \frac{2x+3}{x^{2}+3x+2}\,dx. (a) 12(ln⁡∣x+1∣+ln⁡∣x+2∣)+C\tfrac12\bigl(\ln|x+1|+\ln|x+2|\bigr)+C (b) ln⁡∣x2+3x+2∣+C\ln\bigl|x^{2}+3x+2\bigr|+C (c) ln⁡∣x+1∣−ln⁡∣x+2∣+C\ln|x+1|-\ln|x+2|+C (d) 12 ln⁡∣x2+3x+2∣+C\tfrac12\,\ln|x^{2}+3x+2|+C

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