∫ 1______ cos 2 (x)+a2 sin2(x) dx

3.478 \(\int \frac {1}{\cos ^2(x)+a^2 \sin ^2(x)} \, dx\)

Optimal. Leaf size=9 \[ \frac {\tan ^{-1}(a \tan (x))}{a} \]

[Out]

arctan(a*tan(x))/a

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Rubi [A] time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {203} \[ \frac {\tan ^{-1}(a \tan (x))}{a} \]

Antiderivative was successfully veriﬁed.

[In]

Int[(Cos[x]^2 + a^2*Sin[x]^2)^(-1),x]

[Out]

ArcTan[a*Tan[x]]/a

Rule 203

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTan[(Rt[b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[b, 2]), x] /;

FreeQ[{a, b}, x] && PosQ[a/b] && (GtQ[a, 0] || GtQ[b, 0])

Rubi steps

\begin {align*} \int \frac {1}{\cos ^2(x)+a^2 \sin ^2(x)} \, dx &=\operatorname {Subst}\left (\int \frac {1}{1+a^2 x^2} \, dx,x,\tan (x)\right )\\ &=\frac {\tan ^{-1}(a \tan (x))}{a}\\ \end {align*}

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Mathematica [A] time = 0.03, size = 9, normalized size = 1.00 \[ \frac {\tan ^{-1}(a \tan (x))}{a} \]

Antiderivative was successfully veriﬁed.

[In]

Integrate[(Cos[x]^2 + a^2*Sin[x]^2)^(-1),x]

[Out]

ArcTan[a*Tan[x]]/a

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fricas [B] time = 0.69, size = 35, normalized size = 3.89 \[ -\frac {\arctan \left (\frac {{\left (a^{2} + 1\right )} \cos \relax (x)^{2} - a^{2}}{2 \, a \cos \relax (x) \sin \relax (x)}\right )}{2 \, a} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(cos(x)^2+a^2*sin(x)^2),x, algorithm="fricas")

[Out]

-1/2*arctan(1/2*((a^2 + 1)*cos(x)^2 - a^2)/(a*cos(x)*sin(x)))/a

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giac [B] time = 0.15, size = 20, normalized size = 2.22 \[ \frac {\pi \left \lfloor \frac {x}{\pi } + \frac {1}{2} \right \rfloor + \arctan \left (a \tan \relax (x)\right )}{a} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(cos(x)^2+a^2*sin(x)^2),x, algorithm="giac")

[Out]

(pi*floor(x/pi + 1/2) + arctan(a*tan(x)))/a

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maple [A] time = 0.12, size = 10, normalized size = 1.11 \[ \frac {\arctan \left (a \tan \relax (x )\right )}{a} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(1/(cos(x)^2+a^2*sin(x)^2),x)

[Out]

arctan(a*tan(x))/a

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maxima [A] time = 0.40, size = 9, normalized size = 1.00 \[ \frac {\arctan \left (a \tan \relax (x)\right )}{a} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(cos(x)^2+a^2*sin(x)^2),x, algorithm="maxima")

[Out]

arctan(a*tan(x))/a

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mupad [B] time = 2.83, size = 9, normalized size = 1.00 \[ \frac {\mathrm {atan}\left (a\,\mathrm {tan}\relax (x)\right )}{a} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(1/(cos(x)^2 + a^2*sin(x)^2),x)

[Out]

atan(a*tan(x))/a

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sympy [B] time = 22.40, size = 12007, normalized size = 1334.11 \[ \text {result too large to display} \]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(cos(x)**2+a**2*sin(x)**2),x)

[Out]

Piecewise((64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/

2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2

- 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2

*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt

(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-

2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2

+ 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1))

- 64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a

**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqr

t(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a

**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1

) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 +

2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqr

t(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 64*a**

6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2)

)/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 -

1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a

*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a

**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*

a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 +

2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) +

64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + ta

n(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(

a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2

- 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*

sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sq

rt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a

**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) +

1)) - 112*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))

/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 -

1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*

sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a*

*2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a

**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2

*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) +

112*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**

7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(

-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**

2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1)

+ 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*

a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(

a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 16*a**5*

sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-

2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2

- 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) +

1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqr

t(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a

**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1

) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 16*a**5*sqrt(-2*

a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 -

2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqr

t(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(

-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2

+ 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1)

+ 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) -

2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 80*a**4*sqrt(a**2 - 1)*sq

rt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*

a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 -

2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1

)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(

-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**

2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1)

+ 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 80*a**4*sqrt(a**2

- 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sq

rt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a

**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 -

1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)

*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sq

rt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2

- 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 16*a**4*sqrt

(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*

a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sq

rt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(

a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 -

1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 +

2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sq

rt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 16*a*

*4*sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2)

)/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 -

1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a

*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a

**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*

a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 +

2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) +

56*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a*

*7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt

(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a*

*2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1)

+ 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2

*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt

(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 56*a**3

*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-

2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2

- 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) +

1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqr

t(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a

**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1

) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 20*a**3*sqrt(-2*

a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 -

2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sq

rt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt

(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**

2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1)

+ 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) -

2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 20*a**3*sqrt(-2*a**2 + 2

*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt

(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 -

1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2

+ 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*s

qrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 1

2*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt

(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 24*a**2*sqrt(a**2 - 1)*sqrt(-2*a*

*2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2

*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt

(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-

2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2

+ 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) +

1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2

*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 24*a**2*sqrt(a**2 - 1)*sqr

t(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a*

*2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*

a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*

sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2

*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2

- 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) +

1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 12*a**2*sqrt(a**2 -

1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqr

t(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a*

*2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1

) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*

sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqr

t(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2

- 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 12*a**2*sqrt(

a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a*

*7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt

(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a*

*2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1)

+ 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2

*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt

(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 7*a*sqr

t(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a

**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2

*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)

*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-

2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2

- 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) +

1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 7*a*sqrt(-2*a**2 -

2*a*sqrt(a**2 - 1) + 1)*log(sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqr

t(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2

- 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2

+ 2*a*sqrt(a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*

sqrt(a**2 - 1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) -

12*a**2*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqr

t(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + 5*a*sqrt(-2*a**2 + 2*a*sqrt(a**2

- 1) + 1)*log(-sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1)

+ 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sq

rt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(

a**2 - 1) + 1) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 -

1) + 1) + 36*a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt

(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 -

2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - 5*a*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*l

og(sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*

a**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 +

2*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1

) + 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*

a**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sq

rt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2

- 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log

(-sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a

**2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2

*a*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)

+ 64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a

**3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqr

t(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2

- 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*log(

sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**

2 + 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a

*sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) +

64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**

3*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(

-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 -

1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) - sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(-s

qrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2

+ 2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*

sqrt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) +

64*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3

*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-

2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1

) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)) + sqrt(a**2 - 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)*log(sqr

t(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1) + tan(x/2))/(64*a**7*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 +

2*a*sqrt(a**2 - 1) + 1) - 64*a**6*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sq

rt(a**2 - 1) + 1) - 96*a**5*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 64

*a**4*sqrt(a**2 - 1)*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) + 36*a**3*s

qrt(-2*a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 12*a**2*sqrt(a**2 - 1)*sqrt(-2*

a**2 - 2*a*sqrt(a**2 - 1) + 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1) - 2*a*sqrt(-2*a**2 - 2*a*sqrt(a**2 - 1)

+ 1)*sqrt(-2*a**2 + 2*a*sqrt(a**2 - 1) + 1)), Ne(a, 0)), (-2*tan(x/2)/(tan(x/2)**2 - 1), True))

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