Let . Which of the following equals…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let P(x)=∫x2cos⁡xln⁡(1+t2) dtP(x)=\displaystyle\int_{x^{2}}^{\cos x} \ln(1+t^{2})\,dt. Which of the following equals P′(x)P'(x)? (a) ln⁡(1+cos⁡2x)(sin⁡x)−ln⁡(1+x4)(2x)\ln\bigl(1+\cos^{2}x\bigr)(\sin x)-\ln\bigl(1+x^{4}\bigr)(2x) (b) ln⁡(1+cos⁡2x)(−sin⁡x)−ln⁡(1+x4)(2x)\ln\bigl(1+\cos^{2}x\bigr)(-\sin x)-\ln\bigl(1+x^{4}\bigr)(2x) (c) ln⁡(1+cos⁡2x)(−sin⁡x)−ln⁡(1+x4)(x)\ln\bigl(1+\cos^{2}x\bigr)(-\sin x)-\ln\bigl(1+x^{4}\bigr)(x) (d) ln⁡(1+cos⁡2x)(−sin⁡x)+ln⁡(1+x4)(2x)\ln\bigl(1+\cos^{2}x\bigr)(-\sin x)+\ln\bigl(1+x^{4}\bigr)(2x)

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