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Problem Let P ( x ) = ∫ x 2 cos x ln ( 1 + t 2 ) d t P(x)=\displaystyle\int_{x^{2}}^{\cos x} \ln(1+t^{2})\,dt P ( x ) = ∫ x 2 c o s x ln ( 1 + t 2 ) d t P ′ ( x ) P'(x) P ′ ( x ) ln ( 1 + cos 2 x ) ( sin x ) − ln ( 1 + x 4 ) ( 2 x ) \ln\bigl(1+\cos^{2}x\bigr)(\sin x)-\ln\bigl(1+x^{4}\bigr)(2x) ln ( 1 + cos 2 x ) ( sin x ) − ln ( 1 + x 4 ) ( 2 x ) ln ( 1 + cos 2 x ) ( − sin x ) − ln ( 1 + x 4 ) ( 2 x ) \ln\bigl(1+\cos^{2}x\bigr)(-\sin x)-\ln\bigl(1+x^{4}\bigr)(2x) ln ( 1 + cos 2 x ) ( − sin x ) − ln ( 1 + x 4 ) ( 2 x ) ln ( 1 + cos 2 x ) ( − sin x ) − ln ( 1 + x 4 ) ( x ) \ln\bigl(1+\cos^{2}x\bigr)(-\sin x)-\ln\bigl(1+x^{4}\bigr)(x) ln ( 1 + cos 2 x ) ( − sin x ) − ln ( 1 + x 4 ) ( x ) ln ( 1 + cos 2 x ) ( − sin x ) + ln ( 1 + x 4 ) ( 2 x ) \ln\bigl(1+\cos^{2}x\bigr)(-\sin x)+\ln\bigl(1+x^{4}\bigr)(2x) ln ( 1 + cos 2 x ) ( − sin x ) + ln ( 1 + x 4 ) ( 2 x ) Browse the problem library