3.20 \(\int \frac {1}{a+b \cos ^2(x)} \, dx\)
Optimal. Leaf size=30 \[ -\frac {\tan ^{-1}\left (\frac {\sqrt {a+b} \cot (x)}{\sqrt {a}}\right )}{\sqrt {a} \sqrt {a+b}} \]
[Out]
-arctan(cot(x)*(a+b)^(1/2)/a^(1/2))/a^(1/2)/(a+b)^(1/2)
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Rubi [A] time = 0.02, antiderivative size = 30, normalized size of antiderivative = 1.00,
number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used =
{3181, 205} \[ -\frac {\tan ^{-1}\left (\frac {\sqrt {a+b} \cot (x)}{\sqrt {a}}\right )}{\sqrt {a} \sqrt {a+b}} \]
Antiderivative was successfully verified.
[In]
Int[(a + b*Cos[x]^2)^(-1),x]
[Out]
-(ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]]/(Sqrt[a]*Sqrt[a + b]))
Rule 205
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[a/b, 2]*ArcTan[x/Rt[a/b, 2]])/a, x] /; FreeQ[{a, b}, x]
&& PosQ[a/b]
Rule 3181
Int[((a_) + (b_.)*sin[(e_.) + (f_.)*(x_)]^2)^(-1), x_Symbol] :> With[{ff = FreeFactors[Tan[e + f*x], x]}, Dist
[ff/f, Subst[Int[1/(a + (a + b)*ff^2*x^2), x], x, Tan[e + f*x]/ff], x]] /; FreeQ[{a, b, e, f}, x]
Rubi steps
\begin {align*} \int \frac {1}{a+b \cos ^2(x)} \, dx &=-\operatorname {Subst}\left (\int \frac {1}{a+(a+b) x^2} \, dx,x,\cot (x)\right )\\ &=-\frac {\tan ^{-1}\left (\frac {\sqrt {a+b} \cot (x)}{\sqrt {a}}\right )}{\sqrt {a} \sqrt {a+b}}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 29, normalized size = 0.97 \[ \frac {\tan ^{-1}\left (\frac {\sqrt {a} \tan (x)}{\sqrt {a+b}}\right )}{\sqrt {a} \sqrt {a+b}} \]
Antiderivative was successfully verified.
[In]
Integrate[(a + b*Cos[x]^2)^(-1),x]
[Out]
ArcTan[(Sqrt[a]*Tan[x])/Sqrt[a + b]]/(Sqrt[a]*Sqrt[a + b])
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fricas [B] time = 0.58, size = 163, normalized size = 5.43 \[ \left [-\frac {\sqrt {-a^{2} - a b} \log \left (\frac {{\left (8 \, a^{2} + 8 \, a b + b^{2}\right )} \cos \relax (x)^{4} - 2 \, {\left (4 \, a^{2} + 3 \, a b\right )} \cos \relax (x)^{2} + 4 \, {\left ({\left (2 \, a + b\right )} \cos \relax (x)^{3} - a \cos \relax (x)\right )} \sqrt {-a^{2} - a b} \sin \relax (x) + a^{2}}{b^{2} \cos \relax (x)^{4} + 2 \, a b \cos \relax (x)^{2} + a^{2}}\right )}{4 \, {\left (a^{2} + a b\right )}}, -\frac {\arctan \left (\frac {{\left (2 \, a + b\right )} \cos \relax (x)^{2} - a}{2 \, \sqrt {a^{2} + a b} \cos \relax (x) \sin \relax (x)}\right )}{2 \, \sqrt {a^{2} + a b}}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(a+b*cos(x)^2),x, algorithm="fricas")
[Out]
[-1/4*sqrt(-a^2 - a*b)*log(((8*a^2 + 8*a*b + b^2)*cos(x)^4 - 2*(4*a^2 + 3*a*b)*cos(x)^2 + 4*((2*a + b)*cos(x)^
3 - a*cos(x))*sqrt(-a^2 - a*b)*sin(x) + a^2)/(b^2*cos(x)^4 + 2*a*b*cos(x)^2 + a^2))/(a^2 + a*b), -1/2*arctan(1
/2*((2*a + b)*cos(x)^2 - a)/(sqrt(a^2 + a*b)*cos(x)*sin(x)))/sqrt(a^2 + a*b)]
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giac [A] time = 0.16, size = 37, normalized size = 1.23 \[ \frac {\pi \left \lfloor \frac {x}{\pi } + \frac {1}{2} \right \rfloor \mathrm {sgn}\relax (a) + \arctan \left (\frac {a \tan \relax (x)}{\sqrt {a^{2} + a b}}\right )}{\sqrt {a^{2} + a b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(a+b*cos(x)^2),x, algorithm="giac")
[Out]
(pi*floor(x/pi + 1/2)*sgn(a) + arctan(a*tan(x)/sqrt(a^2 + a*b)))/sqrt(a^2 + a*b)
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maple [A] time = 0.06, size = 21, normalized size = 0.70 \[ \frac {\arctan \left (\frac {a \tan \relax (x )}{\sqrt {\left (a +b \right ) a}}\right )}{\sqrt {\left (a +b \right ) a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(a+b*cos(x)^2),x)
[Out]
1/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))
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maxima [A] time = 0.95, size = 20, normalized size = 0.67 \[ \frac {\arctan \left (\frac {a \tan \relax (x)}{\sqrt {{\left (a + b\right )} a}}\right )}{\sqrt {{\left (a + b\right )} a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(a+b*cos(x)^2),x, algorithm="maxima")
[Out]
arctan(a*tan(x)/sqrt((a + b)*a))/sqrt((a + b)*a)
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mupad [B] time = 2.38, size = 24, normalized size = 0.80 \[ \frac {\mathrm {atan}\left (\frac {a\,\mathrm {tan}\relax (x)}{\sqrt {a^2+b\,a}}\right )}{\sqrt {a^2+b\,a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(a + b*cos(x)^2),x)
[Out]
atan((a*tan(x))/(a*b + a^2)^(1/2))/(a*b + a^2)^(1/2)
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sympy [A] time = 38.28, size = 12026, normalized size = 400.87 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(a+b*cos(x)**2),x)
[Out]
Piecewise((zoo*tan(x/2)/(tan(x/2)**2 - 1), Eq(a, 0) & Eq(b, 0)), (-tan(x/2)/(2*b) + 1/(2*b*tan(x/2)), Eq(a, -b
)), (-2*tan(x/2)/(b*(tan(x/2)**2 - 1)), Eq(a, 0)), (-5*I*a**(5/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) -
a/(a + b) + b/(a + b))*log(-sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/
2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a
+ b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*
sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a
+ b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b)
- a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*s
qrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*
a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b))) + 5*I*a**(5/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(sqrt(2*I*
sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/
(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(
5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) +
b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a +
b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sq
rt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) +
b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a +
b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) - 3*I*a**(5/2)*sqrt(b)
*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(-sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqr
t(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a +
b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(
a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**
3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) +
b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/
(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*
I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) + 3*I*a**(5/2)*sqrt(b)*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) -
a/(a + b) + b/(a + b))*log(sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/
2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a
+ b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*
sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a
+ b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b)
- a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*s
qrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*
a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b))) + 10*I*a**(3/2)*b**(3/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(-sqrt(2
*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(
b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b
**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b
) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a
+ b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I
*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(
a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) - 10*I*a**(3/2)*b**
(3/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))
*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(
a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*s
qrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10
*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b
) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt
(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqr
t(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) - 2*I*a**(3/2)*b**(3/2)*sqrt(2*I*sqrt(a)*sqrt(b)/(a +
b) - a/(a + b) + b/(a + b))*log(-sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*
a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) -
a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqr
t(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(
a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(
-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)
) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(
a + b) + b/(a + b))) + 2*I*a**(3/2)*b**(3/2)*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(sqr
t(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*s
qrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/
2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a
+ b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b
)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt
(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a
+ b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(
b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) - I*sqrt(a)*b**
(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(-sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a
+ b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)
)*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/
(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*
sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 1
0*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqr
t(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sq
rt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) + I*sqrt(a)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b
) - a/(a + b) + b/(a + b))*log(sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**
(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/
(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2
*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b
/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a +
b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*
I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) +
2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b))) + I*sqrt(a)*b**(5/2)*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(-sqrt(-2*
I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b
)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b*
*(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a
+ b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*
sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a
+ b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) - I*sqrt(a)*b**(5/2)
*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) +
b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt
(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b
) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a
)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3
*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b
/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(
a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I
*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) + a**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a
+ b))*log(-sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(
-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)
) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/
(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*
sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b
/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(
a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I
*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) -
a**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))
*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(
a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*s
qrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10
*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b
) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt
(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqr
t(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) + a**3*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) +
b/(a + b))*log(-sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*
sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a
+ b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqr
t(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt
(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b
) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt
(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt
(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b
))) - a**3*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a
/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a
+ b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt
(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-
2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))
- 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(
a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)
*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)
)*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) - 10*a**2*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a
/(a + b) + b/(a + b))*log(-sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2
)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*s
qrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a
+ b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b)
- a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sq
rt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a
*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b))) + 10*a**2*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(sqrt(2*I*sqrt(a)*sqrt
(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/
(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2
*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))
+ 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b
)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*s
qrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) - 2*a**2*b*sqrt(2*I*sqrt(a)*sqrt(b
)/(a + b) - a/(a + b) + b/(a + b))*log(-sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))
/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a
+ b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a +
b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(
a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sq
rt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**
2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/
(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b
) - a/(a + b) + b/(a + b))) + 2*a**2*b*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(sqrt(-2*I
*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)
/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**
(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a +
b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*s
qrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) +
b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a
+ b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) + 5*a*b**2*sqrt(-2*I*
sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(-sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)
) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(
a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/
(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2
*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))
- 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a
/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*s
qrt(b)/(a + b) - a/(a + b) + b/(a + b))) - 5*a*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))
*log(sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sq
rt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I
*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b)
- a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)
*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b
))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b)
- a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a
)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) - 3*a*b*
*2*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*log(-sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b
) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*s
qrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a
+ b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqr
t(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a
**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b
)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(
2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))) + 3*a*b**2*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b)
+ b/(a + b))*log(sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + tan(x/2))/(-8*I*a**(7/2)*sqrt(b)
*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(
a + b)) + 8*I*a**(3/2)*b**(5/2)*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sq
rt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a**4*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqr
t(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**3*b*sqrt(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a +
b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) - 10*a**2*b**2*sqrt(-2*I*sqrt(a)*sqr
t(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b)) + 2*a*b**3*sqr
t(-2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a + b))*sqrt(2*I*sqrt(a)*sqrt(b)/(a + b) - a/(a + b) + b/(a +
b))), True))
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