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Question
Evaluate the following : `int (1)/(7 + 2x^2).dx`
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Solution
I = `int (1)/(7 + 2x^2).dx`
= `(1)/(2) int (1)/(7/2 + x^2).dx`
= `(1)/(2) int (1)/((sqrt(7/2))^2 + x^2).dx`
= `(1)/(2).(1)/((sqrt(7/2))) tan^-1 |x/sqrt(7/2)| + c`
= `(1)/sqrt(14)tan^-1 |(sqrt(2)x)/sqrt(7)| + c`.
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