Question

2 неопределенных интеграла.
Решите.

Answer 1

I hope this helps you

Answer 2

$\int \frac{x^2-3}{2+x^2}\, dx=\int \Big (1-\frac{5}{x^2+2}\Big )dx=x-5\cdot \frac{1}{\sqrt2}\cdot arctg\frac{x}{\sqrt2}+C\\\\\\\int \Big (\frac{3^{x}+4^{x}}{2^{x}}\Big )^2dx=\int \Big ((\frac{3}{2})^{x}+(\frac{4}{2})^{x}\Big )^2dx=\int \Big ((\frac{3}{2})^{x}+2^{x}\Big )^2dx=\\\\=\int \Big ((\frac{3}{2})^{2x}+2\cdot (\frac{3}{2})^{x}\cdot 2^{x}+2^{2x}\Big )dx=\int \Big ((\frac{9}{4})^{x}+2\cdot 3^{x}+4^{x}\Big )dx=\\\\=\frac{(\frac{9}{4})^{x}}{ln\frac{9}{4}}+2\cdot \frac{3^{x}}{ln3}+\frac{4^{x}}{ln4}+C=\frac{9^{x}}{4^{x}\cdot (ln9-ln4)}+\frac{2}{ln3}\cdot 3^{x}+\frac{1}{ln4}\cdot 4^{x}+C$