1.

int_(0)^(3)(3x+1)/(x^(2)+9) dx is equal to

Answer»

`LOG(2sqrt(2))+(pi)/12`
`log(2sqrt(2))+(pi)/2`
`log(2sqrt(2))+(pi)/6`
`log(2sqrt(2))+(pi)/3`

Solution :`int_(0)^(3)(3x+1)/(x^(2)+9)dx=3/2 int_(0)^(3)(2x)/(x^(2)+9)dx`
`+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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