Question

2 неопределенных интеграла.
Решите.

Answer 1

I hope this helps you

Answer 2

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