[m]n=\frac{1}{2}[/m]
[m]p=\frac{1}{2}[/m]
3) случай
[m]\frac{m+1}{n}+p=-1 ∈ [/m]Z
Замена переменной:
[m]1+\sqrt{x}=t^4\sqrt{x}[/m]
⇒[m] \sqrt{x}=\frac{1}{t^4-1}[/m] ⇒[m] x=(t^4-1)^{-2}[/m]
[m]dx=-2(t^4-1)^{-3}\cdot (4t^3)dt[/m]
[m]dx=-\frac{8t^3}{(t^4-1)^3}dt[/m]
[m]t=\sqrt[4]{\frac{1+\sqrt{x}}{\sqrt{x}}}[/m]
[m] ∫ \frac{\sqrt{1+\sqrt{x}}}{x\cdot\sqrt[4]{x^3}}dx= -∫8t^5dt=-8\frac{t:^6}{6}+C=-\frac{4}{3}(\sqrt[4]{\frac{1+\sqrt{x}}{\sqrt{x}}})^6+C=-\frac{4}{3}\frac{(1+\sqrt{x})^{\frac{3}{2}}}{x^{\frac{3}{4}}}+C[/m]