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Question
Evaluate: `int_0^1 (x^2 - 2)/(x^2 + 1).dx`
Solution
`int_0^1 (x^2 - 2)/(x^2 + 1).dx`
= `int_0^1 ((x^2 + 1) - 3)/(x^2 + 1).dx`
= `int_0^1(1 - 3/(x^2 + 1)).dx`
= `int_0^1 1.dx - int_0^1 3/(x^2 + 1).dx`
= `[x]_0^1 - [3 tan^-1x]_0^1`
= (1 – 0) – (3 tan–11 – 3 tan–10)
= `1 - 3(pi/4) - 0`
= `1 - (3pi)/(4)`.
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