int (0)^(3) (3x+1)/(x^(2)+9) dx =...

` int _(0)^(3) (3x+1)/(x^(2)+9) dx = `

A

`log(2sqrt(2))+(pi)/12`

B

`log(2sqrt(2)+(pi)/2`

C

`log(2sqrt(2))+(pi)/6`

D

`log(2sqrt(2))+(pi)/3`

Verified by Experts

The correct Answer is:

A

int (0)^(3) (3x+1)/(x^(2)+9) dx =
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int tan^(-1)((3x-x^(3))/(1-3x^(2)))dx
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int tan^(-1)((3x-x^(3))/(1-3x^(2)))dx
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int(1)/(x^(4)+3x^(2)+9)dx
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int(3x-1)/(sqrt(x^(2)+9))dx
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int (0)^(3) (3x+1)/(x^(2)+9) dx =
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Evalutate : int (x ^(3) +3x ^(2)+x+9)/((x ^(2) +1) (x ^(2) +3))dx.
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int (3x-1)/(sqrt(x^(2)+9))dx
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int(3x^(2))/(9^(2)+x^(3))dx
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