Evaluate the integral .

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

Problem

Evaluate the integral ∫(x+1) ln⁡(2x) dx\displaystyle \int (x+1)\,\ln(2x)\,dx. (a) (x+1)2 ln⁡(2x)−x22−x−12 ln⁡x+C(x+1)^{2}\,\ln(2x) - \dfrac{x^{2}}{2} - x - \dfrac{1}{2}\,\ln x + C (b) (x+1)22 ln⁡(2x)−x28−x2−12 ln⁡x+C\dfrac{(x+1)^{2}}{2}\,\ln(2x) - \dfrac{x^{2}}{8} - \dfrac{x}{2} - \dfrac{1}{2}\,\ln x + C (c) (x+1)22 ln⁡(2x)−x24−x−12 ln⁡x+C\dfrac{(x+1)^{2}}{2}\,\ln(2x) - \dfrac{x^{2}}{4} - x - \dfrac{1}{2}\,\ln x + C (d) (x+1)22 ln⁡(2x)−x24−12 ln⁡x+C\dfrac{(x+1)^{2}}{2}\,\ln(2x) - \dfrac{x^{2}}{4} - \dfrac{1}{2}\,\ln x + C

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