Evaluate ( 12 x^ 3 + 34 x^ 2 -5 x+2 ,dx ).

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Evaluate ∫12x3+34x2−5x+2 dx\displaystyle \int \frac{\tfrac12 x^{3}+\tfrac34 x^{2}-5}{x+2}\,dx. (a) \dfrac{x^{3}}{6}-\dfrac{x^{2}}{8}+\dfrac{x}{2}+6\ln|x+2|+C (b) \dfrac{x^{3}}{6}-\dfrac{x^{2}}{4}+\dfrac{x}{2}-6\ln|x+2|+C (c) \dfrac{x^{3}}{6}-\dfrac{x^{2}}{8}+\dfrac{x}{2}-6\ln|x+2|+C (d) \dfrac{x^{3}}{6}-\dfrac{x^{2}}{8}+\dfrac{x}{2}-3\ln|x+2|+C

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