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Question
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
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Solution
Let I = `int sqrt(x^2 + 2x + 5).dx`
= `int sqrt(x^2 + 2x + 1 + 4)dx`
= `int sqrt((x + 1)^2 + 2^2).dx`
= `((x + 1)/2) int sqrt((x + 1)^2 + 2^2) + 2^2/(2)log|(x + 1) + sqrt((x + 1)^2 + 2^2)| + c`
= `((x + 1)/2)sqrt(x^2 + 2x + 5) + 2log|(x + 1) + sqrt(x^2 + 2x + 5)| + c`.
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