Question

помогите пожалуйста, 26 вариант

Answer 1

$1); ; int frac{dx}{cos^2(15x+9)}=[, t=15x+9; ,; dt=15dx; to ; ; dx=frac{dt}{15}, ]=\\=frac{1}{15}int frac{dt}{cos^2t}=frac{1}{15}cdot tgt+C=frac{1}{15}cdot tg(15x+9)+C\\2); ; int e^{x}cdot 6^{2-e^{x}}dx=[, t=2-e^{x}; ,; dt=-e^{x}dx, ]=\\=-int 6^{t}cdot dt=-frac{6^{t}}{ln6}+C=-frac{6^{2-e^{x}}}{ln6}+C$

$3); ; int frac{x, dx}{25-64x^4}=int frac{x, dx}{5^2-(8x^2)^2} =[, t=8x^2; ,; dt=16x, dx]=\\=frac{1}{16}int frac{dt}{5^2-t^2} =frac{1}{16}cdot frac{1}{10}lnleft |frac{5+t}{5-t}right |+C=\\=frac{1}{160}cdot lnleft |frac{5+8x^2}{5-8x^2}right |+C$