Задача 31207 Помогите пожалуйста решит задачи от 12...
Условие
Все решения
F(x)=(1/(1/5))*(x/5)^(3/2)/(3/2)+4*(1/4)(-cos(4x+2))+C;
[b]F(x)=(10/3)sqrt((x/5)^3) - cos(4x+2) + C[/b]
13.
f(x)=(x^3*(x^2+1)-2)/(x^2+1);
f(x)=x^3 - (2/(x^2+1))
[b]F(x)=(x^4/4) - 2 arctgx + C[/b]
14
f(x)=((x^2+1)-2)/(x^2+1)
f(x)=1 - (2/(x^2+1))
[b]F(x)=x - 2 arctgx + C[/b]
15
1+cosx=2cos^2(x/2)
f(x)=(1/2)*(1/cos^2(x/2))
F(x)=(1/2)/(1/2) * tg(x/2) + C
[b] F(x)=tg(x/2) + C[/b]
16
f(x)=x^3+2x^2-x-2
[b]F(x)=(x^4/4)+2*(x^3/3)-(x^2/2) -2x + C[/b]
17
cos2x=cos^2x-sin^2x
f(x)=(cos^2x-sin^2x)/sin^2x
f(x)=tg^2x - 1
f(x)=(1/cos^2x)-1 -1
f(x)=(1/cos^2x) -2
[b]F(x)=tgx - 2x + C [/b]
18
2cosx*cos5x=2*(1/2)*(cos((x+5x)/2)+cos(x-5x)/2)
cos(-t)=cost - функция четная
f(x)=cos3x+cos2x
F(x)=(1/3)sin3x + (1/2)sin2x + C
19.
tg^2x= (1/cos^2x) - 1
f(x)=(1/cos^2x) - 1
[b[F(x)=tgx - x + C[/b]
23
f(x)=x*x^(1/2)*x^(-3/4)
f(x)=x^(1+(2/4)-(3/4))
f(x)=x^(3/4)
F(x)=x^((3/4)+1)/((3/4)+1)+C
F(x)=(4/7)*x^(7/4) + C
[b] F(x)=(4x*x^(3/4))/7 + C [/b]
24
f(x)=x/sqrt(x) - x^(2/3)/sqrt(x)
f(x)=x^(1/2) - x^(1/6)
F(x)=x^(3/2)/(3/2) - x^(5/3)/(5/3)
[b]F(x)=(2/3)xsqrt(x)) - (3/5)x∛(x^2)[/b]
25
f(x)=3 - 2*(3/2)^x
[b]F(x)=3x-2*(3/2)^x/ln(3/2) + C [/b]
26
f(x)=(2*3*5)^(x)
f(x)=30^(x)
[b]F(x)=(30^(x)/ln30) + C[/b]
27
f(x)=(1+2sqrt(x)+x)/x
f(x)=(1/x)+2sqrt(x)/x + (x)/x
f(x)=(1/x)+(2/sqrt(x))+1
[b]F(x)=ln|x|+4sqrt(x)+x +C[/b]
28
cos(x/2)*sin(3x/2)=(1/2) sin((x/2)-(3x/2))+(1/2)sin((x/2)+(3x/2))
sin(-t)=-sint
f(x)= - (1/2) sinx+(1/2)sin2x
F(x)=(-1/2)(-cosx)+(1/2)*(1/2)(-cos2x) + C
[b]F(x)=(1/2)cosx-(1/4)cos2x+C[/b]