in(div(int(I1),potens(plus(potens(U,int(2)),potens(int(I),int(2))),div(int(1),int(2)))),_,mult(int(I1),ln(plus(U,potens(plus(potens(int(I),int(2)),potens(U,int(2))),div(int(1),int(2))))))):-!.
%23
in(div(int(I1),potens(minus(potens(U,int(2)),potens(int(I),int(2))),div(int(1),int(2)))),_,mult(int(I1),arch(div(U,int(I))))).
%23
in(div(int(I1),potens(minus(potens(U,int(2)),potens(int(I),int(2))),div(int(1),int(2)))),_,mult(int(I1),ln(modul(plus(U,potens(minus(potens(U,int(2)),potens(int(I),int(2))),div(int(1),int(2)))))))):-!.
%3
in(div(int(I),U),X,mult(int(I),div(ln(modul(U)),U1))):d(U,X,U1),!.
%sv-vo5
in(mult(U,V),X,minus(mult(U,V2),R)):in(V,X,V1),reduce(V1,V2),d(U,X,U1),reduce(U1,U2),U2=int(_),in(mult(U2,V2),X,R),!.
in(mult(var(x),V),X,minus(mult(U,V2),R1)):U=var(x),in(V,X,V1),reduce(V1,V2),d(U,X,U1),reduce(U1,U2),in(mult(U2,V2),X,R),reduce(R,R1),!.
in(mult(potens(var(x),int(I)),V),X,minus(mult(U,V2),R)):U=potens(var(x),int(I)),in(V,X,V1),reduce(V1,V2),d(U,X,U1),reduce(U1,U2),in(mult(U2,V2),X,R).
in(mult(V,U),X,minus(mult(U,V2),R)):in(V,X,V1),reduce(V1,V2),d(U,X,U1),reduce(U1,U2),U2=int(_),in(mult(U2,V2),X,R),!.
in(mult(V,var(x)),X,minus(mult(U,V2),R1)):U=var(x),in(V,X,V1),reduce(V1,V2),d(U,X,U1),reduce(U1,U2),in(mult(U2,V2),X,R),reduce(R,R1),!.
in(mult(V,potens(var(x),int(I))),X,minus(mult(U,V2),R)):U=potens(var(x),int(I)),in(V,X,V1),reduce(V1,V2),d(U,X,U1),reduce(U1,U2),in(mult(U2,V2),X,R).
Тесты:
|
Выражение |
Результат |
|
|
1 |
3*(2*x)^5 |
3*(2*x)^6/12 |
|
2 |
17*x^(1/5) |
102*x^(6/5)/5 |
|
3 |
5/(2*x+7) |
5*ln|2*x+7|/2 |
|
4 |
27*e^(2*x+3) |
27*e^(2*x+3)/2 |
|
5 |
5^(3*x+1) |
5^(3*x+1)/(3*ln(5)) |
|
6 |
7*sin(4*x+25) |
0-7*cos(4*x+25)/4 |
|
7 |
15*cos(7*x+25) |
15*sin(7*x+25)/7 |
|
8 |
13*tg(3+7*x) |
0-13*ln|cos(3+7*x)|/7 |
|
9 |
3*ctg(5*x+1) |
3*ln|sin(5*x+1)|/5 |
|
10 |
7/cos(5*x+1)^2 |
7*tg(5*x+1)/5 |
|
11 |
4/sin(5*x+1/2)^2 |
0-4*ctg(5*x+1/2)/5 |
|
12 |
45*sh(1/3+4*x) |
45*ch(1/3+4*x)/4 |
|
13 |
3*ch(x+7/2) |
3*sh(x+7/2) |
|
14 |
5*th(7*x+3/4) |
5*ln(ch(7*x+3/4))/7 |
|
15 |
17*cth(x*2-3) |
17*ln|sh(x*2-3)|/2 |
|
16 |
5/ch(3*x)^2 |
5*th(3*x)/3 |
|
17 |
5/sh(3*x)^2 |
0-5*cth(3*x)/3 |
|
18 |
5/(3^2+x^2) |
5/3*arctg(x/3) |
|
5/(x^2+3^2) |
5/3*arctg(x/3) |
|
|
19 |
5/(3^2-x^2) |
5/3*arth(x/3) (|x|<a) 5/6*ln|(3+x)/(3-x)| |
|
20 |
5/(x^2-3^2) |
5/3*arcth(x/3) (|x|>a) 5/6*ln|(x-3)/(x+3)| |
|
21 |
7/(5^2-x^2)^(1/2) |
7*arcsin(x/5) (|x|<a) |
|
22 |
7/(5^2+x^2)^(1/2) |
7*arsh(x/5) 7*ln(x+(5^2+x^2)^(1/2)) |
|
7/(x^2+5^2)^(1/2) |
7*arsh(x/5) 7*ln(x+(5^2+x^2)^(1/2)) |
|
|
23 |
7/(x^2-5^2)^(1/2) |
7*arch(x/5) 7*ln|x+(x^2-5^2)^(1/2)| |
|
24 |
0.25*tg(7.14*x+0.3*x+1) |
0-0.25*ln|cos(7.14*x+0.3*x+1)|/7.44 |
|
25 |
45*(sh(1/3+4*x)-3*ch(x+7/2)) |
45*ch(1/3+4*x)/4-135*sh(x+7/2) |
|
26 |
cos(3*x)*(x^2) |
x^2*sin(3*x)/3-2*x*(0-cos(3*x)/3)/3-2*(0-sin(3*x)/3/3)/3 |
|
27 |
(x^2)*cos(3*x) |
x^2*sin(3*x)/3-2*x*(0-cos(3*x)/3)/3-2*(0-sin(3*x)/3/3)/3 |
|
28 |
x*e^(0.7*x) |
x*e^(0.7*x)/0.7-e^(0.7*x)/0.7/0.7 |
|
29 |
e^(0.7*x)*x |
x*e^(0.7*x)/0.7-e^(0.7*x)/0.7/0.7 |
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