InterviewSolution
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InterviewSolution
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Evaluate `int(dx)/((5-8x-x^(2)))`. |
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Answer» We have `int(dx)/((5-8x-x^(2)))=-int(dx)/((x^(2)+8x-5))` `=-int(dx)/({(x^(2)+8x+16)-21})=-int(dx)/({(x+4)^(2)-(sqrt(21))^(2)})` `=int(dx)/({(sqrt(21))^(2)-(x+4)^(2)})=int(dt)/({(sqrt(21))^(2)-t^(2)}), "where" (x+4)=t` `=(1)/(2sqrt(21))*log|(sqrt(21)+t)/(sqrt(21)-t)|+C` `=(1)/(2sqrt(21))*log|(sqrt(21)+4+x)/(sqrt(21)-4-x)|+C`. |
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