Найти общий вид первообразной. 4 примера(фото).

[latex]1)\quad f(x)=\frac{\sqrt{x^3}-2}{\sqrt{x}-1} =\frac{(\sqrt{x}-1)(x+\sqrt{x}+1)}{\sqrt{x}-1} =x+\sqrt{x}+1\\\\F(x)=\frac{x^2}{2}+\frac{2x^{\frac{3}{2}}}{3}+x+C\\\\2)\quad f(x)=\frac{sin(\frac{\pi}{6}-2x)}{cos^3(\frac{\pi}{6}-2x)}\\\\F(x)=-\frac{1}{2}\cdot \frac{1}{2cos^2(\frac{\pi}{6}-2x)}+C\\\\3)\quad f(x)=6cos^2(\frac{\pi}{4}-3x)=3(1+cos(\frac{\pi}{2}-6x))=3(1+sin6x)\\\\F(x)=3x-\frac{1}{2}cos6x+C\\\\4)\quad f(x)=10x\sqrt{x}=10x^{\frac{3}{2}}\\\\F(x)=10\cdot \frac{2x^{\frac{5}{2}}}{5}+C=4\sqrt{x^5}+C[/latex] [latex]M_0(1,5):\; \; 5=4\sqrt1+C\; \; \to \; \; C=1\\\\F(x)=4\sqrt{x^5}+1[/latex]