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Question
Evaluate the following integrals : `int(x - 2)/sqrt(x + 5).dx`
Solution
`int(x - 2)/sqrt(x + 5).dx`
= `int((x + 5) - 7)/sqrt(x + 5).dx`
= `int((x + 5)/sqrt(x + 5) - 7/sqrt(x + 5)).dx`
= `int(x + 5)^1/sqrt(x + 5)dx - int7/sqrt(x + 5)dx`
= `int(x + 5)^(1/2) dx - 7 int1/(x + 5)dx`
= `((x + 5)^(1/2 + 1))/((1/2 + 1)) - 7 xx 2sqrt(x + 5) + c`
= `(2)/(3)(x + 5)^(3/2) - 14sqrt(x + 5) + c`
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