3.11.5 \(\int \frac {\sqrt {1+x}}{(1-x)^{13/2}} \, dx\)

Optimal. Leaf size=101 \[ \frac {8 (x+1)^{3/2}}{3465 (1-x)^{3/2}}+\frac {8 (x+1)^{3/2}}{1155 (1-x)^{5/2}}+\frac {4 (x+1)^{3/2}}{231 (1-x)^{7/2}}+\frac {4 (x+1)^{3/2}}{99 (1-x)^{9/2}}+\frac {(x+1)^{3/2}}{11 (1-x)^{11/2}} \]

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Rubi [A]  time = 0.02, antiderivative size = 101, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {45, 37} \begin {gather*} \frac {8 (x+1)^{3/2}}{3465 (1-x)^{3/2}}+\frac {8 (x+1)^{3/2}}{1155 (1-x)^{5/2}}+\frac {4 (x+1)^{3/2}}{231 (1-x)^{7/2}}+\frac {4 (x+1)^{3/2}}{99 (1-x)^{9/2}}+\frac {(x+1)^{3/2}}{11 (1-x)^{11/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Sqrt[1 + x]/(1 - x)^(13/2),x]

[Out]

(1 + x)^(3/2)/(11*(1 - x)^(11/2)) + (4*(1 + x)^(3/2))/(99*(1 - x)^(9/2)) + (4*(1 + x)^(3/2))/(231*(1 - x)^(7/2
)) + (8*(1 + x)^(3/2))/(1155*(1 - x)^(5/2)) + (8*(1 + x)^(3/2))/(3465*(1 - x)^(3/2))

Rule 37

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n +
1))/((b*c - a*d)*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[m + n + 2, 0] && NeQ
[m, -1]

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n + 1
))/((b*c - a*d)*(m + 1)), x] - Dist[(d*Simplify[m + n + 2])/((b*c - a*d)*(m + 1)), Int[(a + b*x)^Simplify[m +
1]*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && ILtQ[Simplify[m + n + 2], 0] &&
NeQ[m, -1] &&  !(LtQ[m, -1] && LtQ[n, -1] && (EqQ[a, 0] || (NeQ[c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && (
SumSimplerQ[m, 1] ||  !SumSimplerQ[n, 1])

Rubi steps

\begin {align*} \int \frac {\sqrt {1+x}}{(1-x)^{13/2}} \, dx &=\frac {(1+x)^{3/2}}{11 (1-x)^{11/2}}+\frac {4}{11} \int \frac {\sqrt {1+x}}{(1-x)^{11/2}} \, dx\\ &=\frac {(1+x)^{3/2}}{11 (1-x)^{11/2}}+\frac {4 (1+x)^{3/2}}{99 (1-x)^{9/2}}+\frac {4}{33} \int \frac {\sqrt {1+x}}{(1-x)^{9/2}} \, dx\\ &=\frac {(1+x)^{3/2}}{11 (1-x)^{11/2}}+\frac {4 (1+x)^{3/2}}{99 (1-x)^{9/2}}+\frac {4 (1+x)^{3/2}}{231 (1-x)^{7/2}}+\frac {8}{231} \int \frac {\sqrt {1+x}}{(1-x)^{7/2}} \, dx\\ &=\frac {(1+x)^{3/2}}{11 (1-x)^{11/2}}+\frac {4 (1+x)^{3/2}}{99 (1-x)^{9/2}}+\frac {4 (1+x)^{3/2}}{231 (1-x)^{7/2}}+\frac {8 (1+x)^{3/2}}{1155 (1-x)^{5/2}}+\frac {8 \int \frac {\sqrt {1+x}}{(1-x)^{5/2}} \, dx}{1155}\\ &=\frac {(1+x)^{3/2}}{11 (1-x)^{11/2}}+\frac {4 (1+x)^{3/2}}{99 (1-x)^{9/2}}+\frac {4 (1+x)^{3/2}}{231 (1-x)^{7/2}}+\frac {8 (1+x)^{3/2}}{1155 (1-x)^{5/2}}+\frac {8 (1+x)^{3/2}}{3465 (1-x)^{3/2}}\\ \end {align*}

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Mathematica [A]  time = 0.02, size = 40, normalized size = 0.40 \begin {gather*} \frac {(x+1)^{3/2} \left (8 x^4-56 x^3+180 x^2-364 x+547\right )}{3465 (1-x)^{11/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Sqrt[1 + x]/(1 - x)^(13/2),x]

[Out]

((1 + x)^(3/2)*(547 - 364*x + 180*x^2 - 56*x^3 + 8*x^4))/(3465*(1 - x)^(11/2))

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IntegrateAlgebraic [A]  time = 0.07, size = 95, normalized size = 0.94 \begin {gather*} \frac {\frac {315 (x+1)^{11/2}}{(1-x)^{11/2}}+\frac {1540 (x+1)^{9/2}}{(1-x)^{9/2}}+\frac {2970 (x+1)^{7/2}}{(1-x)^{7/2}}+\frac {2772 (x+1)^{5/2}}{(1-x)^{5/2}}+\frac {1155 (x+1)^{3/2}}{(1-x)^{3/2}}}{55440} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[Sqrt[1 + x]/(1 - x)^(13/2),x]

[Out]

((1155*(1 + x)^(3/2))/(1 - x)^(3/2) + (2772*(1 + x)^(5/2))/(1 - x)^(5/2) + (2970*(1 + x)^(7/2))/(1 - x)^(7/2)
+ (1540*(1 + x)^(9/2))/(1 - x)^(9/2) + (315*(1 + x)^(11/2))/(1 - x)^(11/2))/55440

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fricas [A]  time = 0.99, size = 100, normalized size = 0.99 \begin {gather*} \frac {547 \, x^{6} - 3282 \, x^{5} + 8205 \, x^{4} - 10940 \, x^{3} + 8205 \, x^{2} + {\left (8 \, x^{5} - 48 \, x^{4} + 124 \, x^{3} - 184 \, x^{2} + 183 \, x + 547\right )} \sqrt {x + 1} \sqrt {-x + 1} - 3282 \, x + 547}{3465 \, {\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1+x)^(1/2)/(1-x)^(13/2),x, algorithm="fricas")

[Out]

1/3465*(547*x^6 - 3282*x^5 + 8205*x^4 - 10940*x^3 + 8205*x^2 + (8*x^5 - 48*x^4 + 124*x^3 - 184*x^2 + 183*x + 5
47)*sqrt(x + 1)*sqrt(-x + 1) - 3282*x + 547)/(x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1)

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giac [A]  time = 1.36, size = 42, normalized size = 0.42 \begin {gather*} \frac {{\left (4 \, {\left ({\left (2 \, {\left (x + 1\right )} {\left (x - 10\right )} + 99\right )} {\left (x + 1\right )} - 231\right )} {\left (x + 1\right )} + 1155\right )} {\left (x + 1\right )}^{\frac {3}{2}} \sqrt {-x + 1}}{3465 \, {\left (x - 1\right )}^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1+x)^(1/2)/(1-x)^(13/2),x, algorithm="giac")

[Out]

1/3465*(4*((2*(x + 1)*(x - 10) + 99)*(x + 1) - 231)*(x + 1) + 1155)*(x + 1)^(3/2)*sqrt(-x + 1)/(x - 1)^6

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maple [A]  time = 0.00, size = 35, normalized size = 0.35 \begin {gather*} \frac {\left (x +1\right )^{\frac {3}{2}} \left (8 x^{4}-56 x^{3}+180 x^{2}-364 x +547\right )}{3465 \left (-x +1\right )^{\frac {11}{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x+1)^(1/2)/(-x+1)^(13/2),x)

[Out]

1/3465*(x+1)^(3/2)*(8*x^4-56*x^3+180*x^2-364*x+547)/(-x+1)^(11/2)

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maxima [B]  time = 1.32, size = 172, normalized size = 1.70 \begin {gather*} \frac {2 \, \sqrt {-x^{2} + 1}}{11 \, {\left (x^{6} - 6 \, x^{5} + 15 \, x^{4} - 20 \, x^{3} + 15 \, x^{2} - 6 \, x + 1\right )}} + \frac {\sqrt {-x^{2} + 1}}{99 \, {\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 5 \, x - 1\right )}} - \frac {4 \, \sqrt {-x^{2} + 1}}{693 \, {\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )}} + \frac {4 \, \sqrt {-x^{2} + 1}}{1155 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} - \frac {8 \, \sqrt {-x^{2} + 1}}{3465 \, {\left (x^{2} - 2 \, x + 1\right )}} + \frac {8 \, \sqrt {-x^{2} + 1}}{3465 \, {\left (x - 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1+x)^(1/2)/(1-x)^(13/2),x, algorithm="maxima")

[Out]

2/11*sqrt(-x^2 + 1)/(x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1) + 1/99*sqrt(-x^2 + 1)/(x^5 - 5*x^4 + 10
*x^3 - 10*x^2 + 5*x - 1) - 4/693*sqrt(-x^2 + 1)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1) + 4/1155*sqrt(-x^2 + 1)/(x^3 -
3*x^2 + 3*x - 1) - 8/3465*sqrt(-x^2 + 1)/(x^2 - 2*x + 1) + 8/3465*sqrt(-x^2 + 1)/(x - 1)

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mupad [B]  time = 0.29, size = 94, normalized size = 0.93 \begin {gather*} \frac {\sqrt {1-x}\,\left (\frac {61\,x\,\sqrt {x+1}}{1155}+\frac {547\,\sqrt {x+1}}{3465}-\frac {184\,x^2\,\sqrt {x+1}}{3465}+\frac {124\,x^3\,\sqrt {x+1}}{3465}-\frac {16\,x^4\,\sqrt {x+1}}{1155}+\frac {8\,x^5\,\sqrt {x+1}}{3465}\right )}{x^6-6\,x^5+15\,x^4-20\,x^3+15\,x^2-6\,x+1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + 1)^(1/2)/(1 - x)^(13/2),x)

[Out]

((1 - x)^(1/2)*((61*x*(x + 1)^(1/2))/1155 + (547*(x + 1)^(1/2))/3465 - (184*x^2*(x + 1)^(1/2))/3465 + (124*x^3
*(x + 1)^(1/2))/3465 - (16*x^4*(x + 1)^(1/2))/1155 + (8*x^5*(x + 1)^(1/2))/3465))/(15*x^2 - 6*x - 20*x^3 + 15*
x^4 - 6*x^5 + x^6 + 1)

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sympy [B]  time = 135.09, size = 3650, normalized size = 36.14

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1+x)**(1/2)/(1-x)**(13/2),x)

[Out]

Piecewise((8*I*(x + 1)**(23/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x -
1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x +
1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3
- 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 184*I*(x + 1)**(21/
2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqr
t(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1
)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x +
1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) + 1932*I*(x + 1)**(19/2)/(3465*sqrt(x - 1)*(x + 1
)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295
200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sq
rt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x -
1)*(x + 1) - 7096320*sqrt(x - 1)) - 12236*I*(x + 1)**(17/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*
(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7
- 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146
361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(
x - 1)) + 52003*I*(x + 1)**(15/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(
x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x
+ 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)
**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 155316*I*(x + 1)
**(13/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 45738
00*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt
(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1
)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) + 329588*I*(x + 1)**(11/2)/(3465*sqrt(x - 1
)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8
+ 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 1463
61600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*s
qrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 488224*I*(x + 1)**(9/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt
(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x
+ 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)*
*4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 70963
20*sqrt(x - 1)) + 479952*I*(x + 1)**(7/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 7623
00*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x
- 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)
*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) - 280896*I
*(x + 1)**(5/2)/(3465*sqrt(x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9
- 4573800*sqrt(x - 1)*(x + 1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 1024531
20*sqrt(x - 1)*(x + 1)**5 - 146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqr
t(x - 1)*(x + 1)**2 + 39029760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)) + 73920*I*(x + 1)**(3/2)/(3465*sqrt(
x - 1)*(x + 1)**11 - 76230*sqrt(x - 1)*(x + 1)**10 + 762300*sqrt(x - 1)*(x + 1)**9 - 4573800*sqrt(x - 1)*(x +
1)**8 + 18295200*sqrt(x - 1)*(x + 1)**7 - 51226560*sqrt(x - 1)*(x + 1)**6 + 102453120*sqrt(x - 1)*(x + 1)**5 -
146361600*sqrt(x - 1)*(x + 1)**4 + 146361600*sqrt(x - 1)*(x + 1)**3 - 97574400*sqrt(x - 1)*(x + 1)**2 + 39029
760*sqrt(x - 1)*(x + 1) - 7096320*sqrt(x - 1)), Abs(x + 1)/2 > 1), (-8*(x + 1)**(23/2)/(3465*sqrt(1 - x)*(x +
1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 1829
5200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*s
qrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 -
x)*(x + 1) - 7096320*sqrt(1 - x)) + 184*(x + 1)**(21/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x
+ 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 -
51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361
600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 -
x)) - 1932*(x + 1)**(19/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)
*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)*
*6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 -
97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) + 12236*(x + 1)**(17/2)/
(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1
- x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(
x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)
**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) - 52003*(x + 1)**(15/2)/(3465*sqrt(1 - x)*(x + 1)**1
1 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*
sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1
- x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(
x + 1) - 7096320*sqrt(1 - x)) + 155316*(x + 1)**(13/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x +
1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51
226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 14636160
0*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x
)) - 329588*(x + 1)**(11/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)
*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)*
*6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 -
97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) + 488224*(x + 1)**(9/2)/
(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1
- x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(
x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)
**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)) - 479952*(x + 1)**(7/2)/(3465*sqrt(1 - x)*(x + 1)**1
1 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*
sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1
- x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(
x + 1) - 7096320*sqrt(1 - x)) + 280896*(x + 1)**(5/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1
)**10 + 762300*sqrt(1 - x)*(x + 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 512
26560*sqrt(1 - x)*(x + 1)**6 + 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600
*sqrt(1 - x)*(x + 1)**3 - 97574400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)
) - 73920*(x + 1)**(3/2)/(3465*sqrt(1 - x)*(x + 1)**11 - 76230*sqrt(1 - x)*(x + 1)**10 + 762300*sqrt(1 - x)*(x
+ 1)**9 - 4573800*sqrt(1 - x)*(x + 1)**8 + 18295200*sqrt(1 - x)*(x + 1)**7 - 51226560*sqrt(1 - x)*(x + 1)**6
+ 102453120*sqrt(1 - x)*(x + 1)**5 - 146361600*sqrt(1 - x)*(x + 1)**4 + 146361600*sqrt(1 - x)*(x + 1)**3 - 975
74400*sqrt(1 - x)*(x + 1)**2 + 39029760*sqrt(1 - x)*(x + 1) - 7096320*sqrt(1 - x)), True))

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