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Question
Find: `int x^2/((x^2 + 9) (x^2 + 16))` dx
Sum
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Solution
`int x^2/((x^2 + 9) (x^2 + 16))` dx
`x^2/((x^2 + 9) (x^2 + 16)) = (-9)/(7(x^2 + 9)) + 16/(7(x^2 + 16))`
= `-9/7 int (dx)/(x^2 + 9) + 16/7 int (dx)/(x^2 + 16)`
= `-3/7tan^-1 x/3 + 4/7 tan^-1 x/4 + C`
∴ `int x^2/((x^2 + 9) (x^2 + 16))dx = 4/7 tan^-1 x/4 -3/7tan^-1 x/3 + C`
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