Define for . What is…

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

Problem

Define H(x)=∫2ln⁡xe3u1+u2 du+x2H(x)=\displaystyle\int_{2}^{\ln x}\frac{e^{3u}}{1+u^{2}}\,du+x^{2} for x>0x>0. What is H′(x)H'(x)? (a) x31+(ln⁡x)2+2x\dfrac{x^{3}}{1+(\ln x)^{2}}+2x (b) −x21+(ln⁡x)2+2x-\dfrac{x^{2}}{1+(\ln x)^{2}}+2x (c) x21+(ln⁡x)2+2x\dfrac{x^{2}}{1+(\ln x)^{2}}+2x (d) x21+(ln⁡x)2\dfrac{x^{2}}{1+(\ln x)^{2}}

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