Question

Кто решит с 8.28 - 8.32 тому 60 балов 10-11 класс

Answer 1

$\int \frac{dx}{9x^2+16}=\int \frac{dx}{(3x)^2+4^2}=\frac{1}{3}\cdot \frac{1}{4}arctg \frac{3x}{4}+C\\\\\int \frac{dx}{\sqrt{x^2+4}} =ln|x+\sqrt{x^2+4}|+C\\\\\int \frac{dx}{\sqrt{4x^2+9}}=\int \frac{dx}{\sqrt{(2x)^2+9}}=\frac{1}{2}\cdot ln|2x+\sqrt{4x^2+9}|+C\\\\\int \frac{dx}{\sqrt{25-x^2}}=\int \frac{dx}{\sqrt{5^2-x^2}}=arcsin\frac{x}{5}+C$

$\int \frac{dx}{5-2x^2}=\int \frac{dx}{(\sqrt5)^2-(\sqrt2x)^2}=\frac{1}{\sqrt2}\cdot \frac{1}{2\sqrt5}\cdot ln\Big |\frac{\sqrt5+\sqrt2x}{\sqrt5-\sqrt2x}\Big |+C$