Compute ( 3x^ 3 +x^ 2 -2x+4 x^ 2 -1 ,dx

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

Compute ∫3x3+x2−2x+4x2−1 dx.\displaystyle \int \frac{3x^{3}+x^{2}-2x+4}{x^{2}-1}\,dx. (a) 32x2+x+3ln⁡∣x+1∣−2ln⁡∣x−1∣+C\dfrac{3}{2}x^{2}+x+3\ln|x+1|-2\ln|x-1|+C (b) 32x2+x+2ln⁡∣x−1∣−3ln⁡∣x+1∣+C\dfrac{3}{2}x^{2}+x+2\ln|x-1|-3\ln|x+1|+C (c) 32x2+x+3ln⁡∣x−1∣−2ln⁡∣x+1∣+C\dfrac{3}{2}x^{2}+x+3\ln|x-1|-2\ln|x+1|+C (d) 32x2+x+3ln⁡∣x−1∣+2ln⁡∣x+1∣+C\dfrac{3}{2}x^{2}+x+3\ln|x-1|+2\ln|x+1|+C

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