MathematicsMedium64×since 2004Q4030The integral ∫e3loge2x+5e2loge2xe4logex+5e3logex−7e2logexdx\int {{{{e^{3{{\log }_e}2x}} + 5{e^{2{{\log }_e}2x}}} \over {{e^{4{{\log }_e}x}} + 5{e^{3{{\log }_e}x}} - 7{e^{2{{\log }_e}x}}}}} dx∫e4logex+5e3logex−7e2logexe3loge2x+5e2loge2xdx, x > 0, is equal to : (where c is a constant of integration)Alogex2+5x−7+c{\log _e}\sqrt {{x^2} + 5x - 7} + clogex2+5x−7+cB4loge∣x2+5x−7∣+c4{\log _e}|{x^2} + 5x - 7| + c4loge∣x2+5x−7∣+cC14loge∣x2+5x−7∣+c{1 \over 4}{\log _e}|{x^2} + 5x - 7| + c41loge∣x2+5x−7∣+cDloge∣x2+5x−7∣+c{\log _e}|{x^2} + 5x - 7| + cloge∣x2+5x−7∣+cCheck answerSkip