Question

Помогите решить а, в, г, д

Answer 1

$1); ; int cos(3x+5)dx=frac{1}{3}sin(3x+5)+C; ;\\2); ; int (underbrace {3-x}_{u})underbrace {cosx, dx}_{dv}=[du=-dx; ,; v=sinx; ]=uv-int v, du=\\=(3-x), sinx-int sinx(-dx)=(3-x), sinx-cosx+C; ;\\3); ; int frac{sqrt3, dx}{9x^2-3}=int frac{sqrt3, dx}{(3x)^2-(sqrt3)^2}=sqrt3cdot frac{1}{2sqrt3}cdot frac{1}{3}cdot lnBig |frac{3x-sqrt3}{3x+sqrt3}Big |+C=\\=frac{1}{6}cdot lnBig |frac{3x-sqrt3}{3x+sqrt3}Big |+C; ;$

$4); ; int e^{1-4x^2}cdot x, dx=[; u=1-4x^2; ,; du=-8x, dx; ]=\\=-frac{1}{8}int e^{u}, du=-frac{1}{8}cdot e^{u}+C=-frac{1}{8}cdot e^{1-4x^2}+C; .\\\P.S.; ; int f(x), dx=F(x)+C; ; Rightarrow ; ; int f(kx+b), dx=frac{1}{k}cdot F(kx+b)+C; .$