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int_(0)^(3)(3x+1)/(x^(2)+9) dx is equal to |
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Answer» `LOG(2sqrt(2))+(pi)/12` `+int_(0)^(3)(dx)/(x^(2)+9)` `[3/2 log(x^(2)+9)+1/3tan^(-1)(x/3)]_(0)^(3)` `=3/2[log(3^(2)+9)-log(0+9)]` `+1/3[TAN^(-1)(3/3)-tan^(-1)0]` `=3/2(log18-log9)+1/3((pi)/4)` `=3/2 log2+(pi)/12=log(2sqrt(2))+(pi)/12` |
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