Задание 6
Вариант
1
>>
f = 9*x^2/(x^2 + 1)
f
=
9*x^2/(x^2+1)
>>
int(f,x)
ans
=
9*x-9*atan(x)
Вариант
2
dx
>>
f = (17*x^2 + 14)*cos(9*x);
>>
int(f,x)
ans
=
17/9*x^2*sin(9*x)+1100/729*sin(9*x)+34/81*x*cos(9*x)
Вариант
3
dx
>>syms
x
>>int(sqrt(4-x^2),x)
Ans=
1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)
>>[m]=simple(ans)
m=
1/2*x*(4-x^2)^(1/2)+2*asin(1/2*x)
Вариант
4
>>
f = sqrt(1+x^2)/(2+x^2)
f
=
(x^2+1)^(1/2)/(2+x^2)
>>
int(f,x)
ans
=
asinh(x)-1/2*2^(1/2)*atanh(1/2*2^(1/2)*x/(x^2+1)^(1/2))
Вариант
5
>>
f = 1/((x^2 + 4)*sqrt(4*x^2))
f
=
1/2/(x^2+4)/(x^2)^(1/2)
>>
int(f,x)
ans
=
1/16*x*(2*log(x)-log(x^2+4))/(x^2)^(1/2)
>>
pretty(ans)
>>
simple(ans)
Вариант
6
dx
>>syms
x
>>int((x^2+1)/(sqrt(x^2-4*x+1)),x)
Ans=
1/2*x*(x^2-4*x+1)^(1/2)+3*(x^2-4*x+1)^(1/2)+13/2*log(x-2+((x^2-4*x+1)^(1/2))
Вариант
7
dx
>>syms
x
>>int((x^3+1)*log(x),x)
Ans=
1/4*x^4*log(x)-1/16*x^4+x*log(x)-x
Вариант
11
11.
dx
>>
int(1/(cos(x)*(1-sin(x))),x)
ans
=
1/(tan(1/2*x)-1)^2+1/(tan(1/2*x)-1)-1/2*log(tan(1/2*x)-1)+1/2*log(tan(1/2*x)+1)
Вариант
13
>>
f = log(atan(x))/(x^2 + 1);
>>
int(f,x)
ans
=
atan(x)*log(atan(x))-atan(x)
>>
17
