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

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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 \( (x-\beta) u \)
\( \int \frac{\left(x+\sqrt{1+x^{2}}\right)^{15}}{\sqrt{1+x^{2}}} d x \) is equal to
(1) \( \frac{\left(x+\sqrt{\left.1+x^{2}\right)^{16}}\right.}{10}+C \)
(2) \( \frac{1}{15 \sqrt{1+x^{2}+x}}+C \)
(3) \( \frac{15}{\left(\sqrt{1+x^{2}-x}\right.}+C \)
(4)
\( \frac{\left(x+\sqrt{1+x^{2}}\right)^{15}}{15}+C \)
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