digerdiga

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These are questions asked by digerdiga

I want to calculate the below triple integral numerically. I tried different methods and reduced accuracy but nothing works.

Anyone capable?

Thanks

 

restart;
Digits := 15;
with(VectorCalculus);
v1 := <0, 0, 1>;
v2 := <sin(theta2), 0, cos(theta2)>;
v3 := <VectorCalculus:-`*`(sin(theta3), cos(phi3)), VectorCalculus:-`*`(sin(theta3), sin(phi3)), cos(theta3)>;
v1v2 := CrossProduct(v1, v2);
v2v3 := CrossProduct(v3, v2);
DotProduct(v1v2, v2v3);
(simplify(VectorCalculus:-`*`(%, VectorCalculus:-`*`(Norm(v1v2), Norm(v2v3))^VectorCalculus:-`-`(1))) assuming (0 < theta2, theta2 < Pi, 0 < theta3, theta3 < Pi));
evalf(VectorCalculus:-`*`(Int(VectorCalculus:-`*`(arccos(%), sin(theta3)), [theta2 = 0 .. Pi, theta3 = 0 .. Pi, phi3 = 0 .. VectorCalculus:-`*`(2, Pi)], epsilon = 0.001, method = _d01akc), VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(2, Pi), 2), Pi), 4), Pi)^VectorCalculus:-`-`(1)));

Hey,

Is anyone of you capable of simplifying this expression

f1:=(-3*sin(8*x) + 3*sin(8*x + 2*y) - 3*sin(8*x + 6*y) + 3*sin(8*y + 8*x) + 3*sin(8*y + 6*x) + 3*sin(8*y) - 18*sin(8*y + 4*x) + 3*sin(8*y + 2*x) - 45*sin(6*y + 6*x) + 87*sin(4*y + 6*x) - 3*sin(6*x - 2*y) - 87*sin(6*x + 2*y) + 18*sin(4*x - 4*y) - 93*sin(4*x + 4*y) + 93*sin(4*x + 6*y) - 51*sin(2*x - 4*y) - 342*sin(2*x + 4*y) - 3*sin(-6*y + 2*x) + 51*sin(6*y + 2*x) - 93*sin(-2*y + 4*x) + 342*sin(-2*y + 2*x) + 639*sin(2*x + 2*y) - 639*sin(2*x) + 45*sin(6*x) + 93*sin(4*x) + 231*sin(4*y) - 225*sin(2*y) - 63*sin(6*y) - 57*sqrt(3)*cos(2*x) - 375*sqrt(3)*cos(2*y) + sqrt(3)*cos(8*y + 8*x) - 5*sqrt(3)*cos(8*x + 6*y) - 7*sqrt(3)*cos(8*y + 6*x) + sqrt(3)*cos(8*x) + 192*sqrt(3)*cos(2*y + 4*x) + 43*sqrt(3)*cos(-2*y + 4*x) - 7*sqrt(3)*cos(6*x + 2*y) + 7*sqrt(3)*cos(-6*y + 2*x) - 5*sqrt(3)*cos(6*y) - 149*sqrt(3)*cos(4*x + 4*y) - 149*sqrt(3)*cos(4*x) - 65*sqrt(3)*cos(6*y + 2*x) + 126*sqrt(3)*cos(2*x + 4*y) - 65*sqrt(3)*cos(2*x - 4*y) - 5*sqrt(3)*cos(8*x + 2*y) - sqrt(3)*cos(8*y) + 7*sqrt(3)*cos(8*y + 2*x) + 6*sqrt(3)*cos(8*x + 4*y) - 57*sqrt(3)*cos(2*x + 2*y) + 125*sqrt(3)*cos(4*y) + 126*sqrt(3)*cos(-2*y + 2*x) - 7*sqrt(3)*cos(6*x - 2*y) + 19*sqrt(3)*cos(6*x) + 43*sqrt(3)*cos(4*x + 6*y) + 19*sqrt(3)*cos(6*y + 6*x) - 7*sqrt(3)*cos(4*y + 6*x) + 246*sqrt(3))/(2*(-261*sin(4*x + y) - 297*sin(2*x + 3*y) - 48*sin(5*y + 6*x) + 126*sin(5*y + 2*x) + 9*sin(5*y + 8*x) + 12*sin(7*y + 6*x) - 9*sin(7*y + 4*x) - 36*sin(5*y + 4*x) + 261*sin(3*y + 4*x) + 9*sin(-3*y + 4*x) + 297*sin(-y + 2*x) - 135*sin(3*y) - 21*sin(5*y) - 147*cos(y)*sqrt(3) - 9*sqrt(3)*cos(7*y + 4*x) - 3*sqrt(3)*cos(5*y + 8*x) - 3*sqrt(3)*cos(3*y + 8*x) + 54*sqrt(3)*cos(6*x + 3*y) + 5*sqrt(3)*cos(-5*y + 2*x) + 5*sqrt(3)*cos(7*y + 2*x) - 2*sqrt(3)*cos(6*x - y) - 20*sqrt(3)*cos(6*x + y) - 69*sqrt(3)*cos(4*x + y) + 68*sqrt(3)*cos(4*x - y) + 2*sqrt(3)*cos(8*x + y) + 2*sqrt(3)*cos(7*y + 8*x) - 20*sqrt(3)*cos(5*y + 6*x) - 2*sqrt(3)*cos(7*y + 6*x) + 68*sqrt(3)*cos(5*y + 4*x) - 9*sqrt(3)*cos(-3*y + 4*x) - 69*sqrt(3)*cos(3*y + 4*x) - 171*sqrt(3)*cos(2*x + 3*y) - 35*sqrt(3)*cos(5*y) + 171*sqrt(3)*cos(3*y) - 171*sqrt(3)*cos(-y + 2*x) + 354*sqrt(3)*cos(2*x + y) + sqrt(3)*cos(7*y) + 639*sin(y) - 9*sin(3*y + 8*x) - 12*sin(6*x - y) + 3*sin(7*y) - 9*sin(7*y + 2*x) + 9*sin(-5*y + 2*x) + 48*sin(6*x + y) + 36*sin(4*x - y) - 126*sin(2*x - 3*y)))

 

into

 

cos(y-Pi/3).

 

PS: Actually I managed by expanding the thing out and converting to exp then expanding again and using radnormal. In essence I leave the question, because maybe somebody can explain to me why radnormal seems to be superior (sometimes) to simplify which I thought of as the USEALL choice. Thanks

Why doesn't

f:=ln(s + 2)^2 + 2*polylog(2, -1 - s) + 2*polylog(2, (1 + s)/(s + 2))

simplify to zero assuming s>0?

How do I get Maple to factorize this simple expression without too much effort?

f:=3/2 + sqrt(8*k + 2) + 2*k

So I have this expression

f:=(coth(x)^(1/3)-tanh(x)^(1/3))*(coth(x)^(2/3)+tanh(x)^(2/3)+1)

which Maple can not simplify?

I need to do it like this

`assuming`([expand(simplify(add(`~`[simplify]([op(combine(expand((coth(x)^(1/3)-tanh(x)^(1/3))*(coth(x)^(2/3)+tanh(x)^(2/3)+1))))]))))], [x > 1])

Is this actually true or what is happening here?

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