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Evaluate : ∫x^2 (x^2+4) (x^2+9)dx - Mathematics

Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`

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Solution

 

`int x^2/((x^2+4)(x^2+9))dx=int[-4/(5(x^2+4))+9/(5(x^2+9))]dx=int-4/(5(x^2+4))dx+int9/(5(x^2+9))dx`

`=-4/5xx1/2 tan^(-1)(x/2)+9/5xx1/3tan^(-1)(x/3)+C`

`=-2/5tan^(-1)x/2+3/5tan^(-1)x/3+C`

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