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Evaluate: int1/((x^2+2)(x^2+5))\ dx...

Evaluate: `int1/((x^2+2)(x^2+5))\ dx`

Text Solution

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Given integration,
`I=int1/((x^2+2)(x^2+5))\ dx`
`=1/3int(1/(x^2+2)-1/(x^2+5))dx`
`=1/3 int(1/(x^2+(sqrt2)^2)-1/(x^2+(sqrt5)^2))dx`
`=1/3 (1/sqrt2 tan^-1(x/sqrt2)-1/sqrt5 tan ^-1 (x/sqrt5)+c)`
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