Determine ( 3x^ 3 -x^ 2 +2 x^ 2 -4 ,dx

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

Problem

Determine ∫3x3−x2+2x2−4 dx.\displaystyle \int \frac{3x^{3}-x^{2}+2}{x^{2}-4}\,dx. (a) 32x2−x+132ln⁡∣x−2∣+112ln⁡∣x+2∣+C\dfrac{3}{2}x^{2}-x+\tfrac{13}{2}\ln|x-2|+\tfrac{11}{2}\ln|x+2|+C (b) 32x2−x+112ln⁡∣x−2∣−132ln⁡∣x+2∣+C\dfrac{3}{2}x^{2}-x+\tfrac{11}{2}\ln|x-2|-\tfrac{13}{2}\ln|x+2|+C (c) 32x2−x+11ln⁡∣x−2∣+13ln⁡∣x+2∣+C\dfrac{3}{2}x^{2}-x+11\ln|x-2|+13\ln|x+2|+C (d) 32x2−x+112ln⁡∣x−2∣+132ln⁡∣x+2∣+C\dfrac{3}{2}x^{2}-x+\tfrac{11}{2}\ln|x-2|+\tfrac{13}{2}\ln|x+2|+C

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