Question

Срочно 30 баллов
Нужно решить методом который указан

Answer 1

$1. int e^{cos(2x+4)}sin(2x+4):dx =\t = 2x+4, ;dt = 2:dx\= frac12cdotint e^{cos t}sin t:dt =\u = cos t, ;du = -sin t:dt\= -frac12cdotint e^u:du = -frac12cdot e^u + C = -frac12cdot e^{cos(2x+4)} + C$

$2. int xsqrt[4]{2+x^2}:dx =\t = 2 +x^2, ;dt = 2x:dx\= frac12intsqrt[4]{t}:dt = frac12int t^{frac14}:dt = frac12cdotfrac45cdot t^{frac54} + C = frac25cdotsqrt[4]{t^5} + C = frac25cdotsqrt[4]{(2+x^2)^5} + C$

$3. intfrac{cos 3x:dx}{sqrt{5+4sin 3x}} = \\t = 5 + 4sin3x, ;dt = 12cos3x:dx\= frac1{12}intfrac{dt}{sqrt t} = frac1{12}int t^{-frac12}:dt = frac16cdotsqrt t + C = frac16cdotsqrt{5+4sin 3x} + C$