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Paragraph for Let us consider the integral of the
\( \mathrm{P} \) following forms \( f\left(x_{1}, \sqrt{m x^{2}+n x+p}\right. \)

W.
Case I If \( m0 \), then put \( \sqrt{m x^{2}+n x+p}=u \pm x \sqrt{m} \)
Case II If \( p0 \), then put \( \sqrt{m x^{2}+n x+p}=u x \pm \sqrt{p} \)
Case III If quadratic equation \( m x^{2}+n x+p=0 \)
has real roots \( \alpha \) and \( \beta \) there put \( \sqrt{m x^{2}+n x+p} \)
\( =(x-\alpha) \) u or \( (x-\beta) u \)
If \( I=\int \frac{d x}{x-\sqrt{9 x^{2}+4 x+6}} \) To evaluate I, one of the
most proper substitution could be
(1) \( \sqrt{9 x^{2}+4 x+6}=u \pm 3 x \)
(2) \( \sqrt{9 x^{2}+4 x+6}=3 u \pm x \)
(3) \( \quad x=\frac{1}{t} \)
(4) \( 9 x^{2}+4 x+6=\frac{1}{t} \)
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