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Problem The value of ∫ 0 2 d x ( 17 + 8 x − 4 x 2 ) ( e 6 ( 1 − x ) + 1 ) \int_{0}^{2} \frac{dx}{(17+8x-4x^2)(e^{6(1-x)}+1)} ∫ 0 2 ( 17 + 8 x − 4 x 2 ) ( e 6 ( 1 − x ) + 1 ) d x − 1 8 21 log ∣ 2 − 21 2 + 21 ∣ -\frac{1}{8\sqrt{21}} \log \left| \frac{2-\sqrt{21}}{2+\sqrt{21}} \right| − 8 21 1 log 2 + 21 2 − 21 − 1 8 21 log ∣ 2 + 21 21 − 2 ∣ -\frac{1}{8\sqrt{21}} \log \left| \frac{2+\sqrt{21}}{\sqrt{21}-2} \right| − 8 21 1 log 21 − 2 2 + 21 − 1 8 21 { log ∣ 2 − 21 2 + 21 ∣ − log ∣ 2 + 21 21 − 2 ∣ } -\frac{1}{8\sqrt{21}} \left\{ \log \left| \frac{2-\sqrt{21}}{2+\sqrt{21}} \right| - \log \left| \frac{2+\sqrt{21}}{\sqrt{21}-2} \right| \right\} − 8 21 1 { log 2 + 21 2 − 21 − log 21 − 2 2 + 21 } Browse the problem library