InterviewSolution
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InterviewSolution
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`int_(0)^(2)(dx)/(x+4-x^(2))` |
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Answer» `int_(0)^(2)(1)/(x+4-x^(2))dx` `=int_(0)^(2)(1)/(x+4-x^(2)-((1)/(2))^(2)+((1)/(2))^(2))dx` `=int_(0)^(2)(1)/(4+(1)/(4)-[(x^(2)-x+(1)/(4))])dx` `=int_(0)^(2)(1)/(((sqrt(17))/(2))^(2)-(x-(1)/(2))^(2))dx` `=(1)/(2.(sqrt(17))/(2))[log|((sqrt(17))/(2)+x-(1)/(2))/((sqrt(17))/(2)-x+(1)/(2))|]_(0)^(2)` `=(1)/(sqrt(17))[log|(sqrt(17)+2x-1)/(sqrt(17)-2x+1)|]_(0)^(2)` `=(1)/(sqrt(17))[log|(sqrt(17)+3)/(sqrt(17)-3)-log|(sqrt(17)-1)/(sqrt(17)+1)|]` `=(1)/(sqrt(17))log|(sqrt(17)+3)/(sqrt(17)-3)div(sqrt(17)-1)/(sqrt(17+1))|` `(1)/(sqrt(17))log|((sqrt(17)+3)(sqrt(17)+1))/((sqrt(17-3))(sqrt(17)-1))|` `=(1)/(sqrt(17))log|(20+4sqrt(17))/(20-4sqrt(17))|` `=(1)/(sqrt(17))log|(5+sqrt(17))/(5-sqrt(17))xx(5+sqrt(17))/(5+sqrt(17))|` `=(1)/(sqrt(17))log|((5+sqrt(17))^(2))/((5)^(2)-(sqrt(17))^(2))|` `" "[because (a-b)(a+b)=a^(2)-b^(2)]` `=(1)/(sqrt(17))log|(25+17+10sqrt(17))/(25-17)|` `=(1)/(sqrt(17))log|(42+10sqrt(17))/(8)|` `=(1)/(sqrt(17))log|(21+5sqrt(17))/(4)|` |
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