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Question
Integrate the following with respect to x.
`(6x + 7)/sqrt(3x^2 + 7x - 1)`
Solution
Let f(x) = 3x2 + 7x – 1
Then f'(x) = 6x + 7
So `int (6x + 7)/sqrt(3x^2 + 7x - 1) "d"x = int ("f'"(x))/("f"(x)) "d"x`
= `2sqrt("f"(x) + "c")`
= `2sqrt(3x^2 + 7x - 1 + "c")`
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