Let #160; = ∫dx√( (x^2 + 6x 7)) =∫dx√( ([x+3]^2 16)) =∫dx√((4)^2 (x+3)^2) =sin^ 1(x+34)+C ...

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Integration of Irrational Algebraic Fractions - 1

∫dx√7-6x-x2

Question

$\int \frac{d x}{\sqrt{7 - 6 x - x^{2}}}$

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Solution

Let
$= \int \frac{d x}{\sqrt{- (x^{2} + 6 x - 7)}}$
$= \int \frac{d x}{\sqrt{- ([x + 3]^{2} - 16)}}$
$= \int \frac{d x}{\sqrt{(4)^{2} - (x + 3)^{2}}}$
$= s i n^{- 1} (\frac{x + 3}{4}) + C$

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