3.273 \(\int \frac {1}{1-\sinh ^5(x)} \, dx\)
Optimal. Leaf size=228 \[ -\frac {2 \tanh ^{-1}\left (\frac {(-1)^{3/5}-\tanh \left (\frac {x}{2}\right )}{\sqrt {1-\sqrt [5]{-1}}}\right )}{5 \sqrt {1-\sqrt [5]{-1}}}+\frac {1}{5} \sqrt {2} \tanh ^{-1}\left (\frac {\tanh \left (\frac {x}{2}\right )+1}{\sqrt {2}}\right )+\frac {2 \tanh ^{-1}\left (\frac {\tanh \left (\frac {x}{2}\right )+(-1)^{4/5}}{\sqrt {1-(-1)^{3/5}}}\right )}{5 \sqrt {1-(-1)^{3/5}}}-\frac {2 \sqrt [10]{-1} \tanh ^{-1}\left (\frac {(-1)^{3/10} \left ((-1)^{4/5} \tanh \left (\frac {x}{2}\right )+1\right )}{\sqrt {\sqrt [5]{-1}+(-1)^{3/5}}}\right )}{5 \sqrt {\sqrt [5]{-1}+(-1)^{3/5}}}-\frac {2 \sqrt [10]{-1} \tan ^{-1}\left (\frac {\sqrt [10]{-1} \tanh \left (\frac {x}{2}\right )+i}{\sqrt {1-\sqrt [5]{-1}}}\right )}{5 \sqrt {1-\sqrt [5]{-1}}} \]
[Out]
1/5*arctanh(1/2*(1+tanh(1/2*x))*2^(1/2))*2^(1/2)-2/5*(-1)^(1/10)*arctan((I+(-1)^(1/10)*tanh(1/2*x))/(1-(-1)^(1
/5))^(1/2))/(1-(-1)^(1/5))^(1/2)-2/5*arctanh(((-1)^(3/5)-tanh(1/2*x))/(1-(-1)^(1/5))^(1/2))/(1-(-1)^(1/5))^(1/
2)+2/5*arctanh(((-1)^(4/5)+tanh(1/2*x))/(1-(-1)^(3/5))^(1/2))/(1-(-1)^(3/5))^(1/2)-2/5*(-1)^(1/10)*arctanh((-1
)^(3/10)*(1+(-1)^(4/5)*tanh(1/2*x))/((-1)^(1/5)+(-1)^(3/5))^(1/2))/((-1)^(1/5)+(-1)^(3/5))^(1/2)
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Rubi [A] time = 0.42, antiderivative size = 228, normalized size of antiderivative = 1.00,
number of steps used = 17, number of rules used = 6, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.600, Rules used
= {3213, 2660, 618, 204, 617, 206} \[ -\frac {2 \tanh ^{-1}\left (\frac {(-1)^{3/5}-\tanh \left (\frac {x}{2}\right )}{\sqrt {1-\sqrt [5]{-1}}}\right )}{5 \sqrt {1-\sqrt [5]{-1}}}+\frac {1}{5} \sqrt {2} \tanh ^{-1}\left (\frac {\tanh \left (\frac {x}{2}\right )+1}{\sqrt {2}}\right )+\frac {2 \tanh ^{-1}\left (\frac {\tanh \left (\frac {x}{2}\right )+(-1)^{4/5}}{\sqrt {1-(-1)^{3/5}}}\right )}{5 \sqrt {1-(-1)^{3/5}}}-\frac {2 \sqrt [10]{-1} \tanh ^{-1}\left (\frac {(-1)^{3/10} \left ((-1)^{4/5} \tanh \left (\frac {x}{2}\right )+1\right )}{\sqrt {\sqrt [5]{-1}+(-1)^{3/5}}}\right )}{5 \sqrt {\sqrt [5]{-1}+(-1)^{3/5}}}-\frac {2 \sqrt [10]{-1} \tan ^{-1}\left (\frac {\sqrt [10]{-1} \tanh \left (\frac {x}{2}\right )+i}{\sqrt {1-\sqrt [5]{-1}}}\right )}{5 \sqrt {1-\sqrt [5]{-1}}} \]
Antiderivative was successfully verified.
[In]
Int[(1 - Sinh[x]^5)^(-1),x]
[Out]
(-2*(-1)^(1/10)*ArcTan[(I + (-1)^(1/10)*Tanh[x/2])/Sqrt[1 - (-1)^(1/5)]])/(5*Sqrt[1 - (-1)^(1/5)]) - (2*ArcTan
h[((-1)^(3/5) - Tanh[x/2])/Sqrt[1 - (-1)^(1/5)]])/(5*Sqrt[1 - (-1)^(1/5)]) + (Sqrt[2]*ArcTanh[(1 + Tanh[x/2])/
Sqrt[2]])/5 + (2*ArcTanh[((-1)^(4/5) + Tanh[x/2])/Sqrt[1 - (-1)^(3/5)]])/(5*Sqrt[1 - (-1)^(3/5)]) - (2*(-1)^(1
/10)*ArcTanh[((-1)^(3/10)*(1 + (-1)^(4/5)*Tanh[x/2]))/Sqrt[(-1)^(1/5) + (-1)^(3/5)]])/(5*Sqrt[(-1)^(1/5) + (-1
)^(3/5)])
Rule 204
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /
; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])
Rule 206
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])
Rule 617
Int[((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> With[{q = 1 - 4*Simplify[(a*c)/b^2]}, Dist[-2/b, Sub
st[Int[1/(q - x^2), x], x, 1 + (2*c*x)/b], x] /; RationalQ[q] && (EqQ[q^2, 1] || !RationalQ[b^2 - 4*a*c])] /;
FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]
Rule 618
Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]
Rule 2660
Int[((a_) + (b_.)*sin[(c_.) + (d_.)*(x_)])^(-1), x_Symbol] :> With[{e = FreeFactors[Tan[(c + d*x)/2], x]}, Dis
t[(2*e)/d, Subst[Int[1/(a + 2*b*e*x + a*e^2*x^2), x], x, Tan[(c + d*x)/2]/e], x]] /; FreeQ[{a, b, c, d}, x] &&
NeQ[a^2 - b^2, 0]
Rule 3213
Int[((a_) + (b_.)*((c_.)*sin[(e_.) + (f_.)*(x_)])^(n_))^(p_), x_Symbol] :> Int[ExpandTrig[(a + b*(c*sin[e + f*
x])^n)^p, x], x] /; FreeQ[{a, b, c, e, f, n}, x] && (IGtQ[p, 0] || (EqQ[p, -1] && IntegerQ[n]))
Rubi steps
\begin {align*} \int \frac {1}{1-\sinh ^5(x)} \, dx &=\int \left (\frac {\sqrt [10]{-1}}{5 \left (\sqrt [10]{-1}-i \sinh (x)\right )}+\frac {\sqrt [10]{-1}}{5 \left (\sqrt [10]{-1}-\sqrt [10]{-1} \sinh (x)\right )}+\frac {\sqrt [10]{-1}}{5 \left (\sqrt [10]{-1}+(-1)^{3/10} \sinh (x)\right )}+\frac {\sqrt [10]{-1}}{5 \left (\sqrt [10]{-1}+(-1)^{7/10} \sinh (x)\right )}+\frac {\sqrt [10]{-1}}{5 \left (\sqrt [10]{-1}-(-1)^{9/10} \sinh (x)\right )}\right ) \, dx\\ &=\frac {1}{5} \sqrt [10]{-1} \int \frac {1}{\sqrt [10]{-1}-i \sinh (x)} \, dx+\frac {1}{5} \sqrt [10]{-1} \int \frac {1}{\sqrt [10]{-1}-\sqrt [10]{-1} \sinh (x)} \, dx+\frac {1}{5} \sqrt [10]{-1} \int \frac {1}{\sqrt [10]{-1}+(-1)^{3/10} \sinh (x)} \, dx+\frac {1}{5} \sqrt [10]{-1} \int \frac {1}{\sqrt [10]{-1}+(-1)^{7/10} \sinh (x)} \, dx+\frac {1}{5} \sqrt [10]{-1} \int \frac {1}{\sqrt [10]{-1}-(-1)^{9/10} \sinh (x)} \, dx\\ &=\frac {1}{5} \left (2 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt [10]{-1}-2 i x-\sqrt [10]{-1} x^2} \, dx,x,\tanh \left (\frac {x}{2}\right )\right )+\frac {1}{5} \left (2 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt [10]{-1}-2 \sqrt [10]{-1} x-\sqrt [10]{-1} x^2} \, dx,x,\tanh \left (\frac {x}{2}\right )\right )+\frac {1}{5} \left (2 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt [10]{-1}+2 (-1)^{3/10} x-\sqrt [10]{-1} x^2} \, dx,x,\tanh \left (\frac {x}{2}\right )\right )+\frac {1}{5} \left (2 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt [10]{-1}+2 (-1)^{7/10} x-\sqrt [10]{-1} x^2} \, dx,x,\tanh \left (\frac {x}{2}\right )\right )+\frac {1}{5} \left (2 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt [10]{-1}-2 (-1)^{9/10} x-\sqrt [10]{-1} x^2} \, dx,x,\tanh \left (\frac {x}{2}\right )\right )\\ &=\frac {2}{5} \operatorname {Subst}\left (\int \frac {1}{2-x^2} \, dx,x,1+\tanh \left (\frac {x}{2}\right )\right )-\frac {1}{5} \left (4 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{-4 \left (1-\sqrt [5]{-1}\right )-x^2} \, dx,x,-2 i-2 \sqrt [10]{-1} \tanh \left (\frac {x}{2}\right )\right )-\frac {1}{5} \left (4 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{4 \sqrt [5]{-1} \left (1-\sqrt [5]{-1}\right )-x^2} \, dx,x,2 (-1)^{7/10}-2 \sqrt [10]{-1} \tanh \left (\frac {x}{2}\right )\right )-\frac {1}{5} \left (4 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{4 \sqrt [5]{-1} \left (1-(-1)^{3/5}\right )-x^2} \, dx,x,-2 (-1)^{9/10}-2 \sqrt [10]{-1} \tanh \left (\frac {x}{2}\right )\right )-\frac {1}{5} \left (4 \sqrt [10]{-1}\right ) \operatorname {Subst}\left (\int \frac {1}{4 \left (\sqrt [5]{-1}+(-1)^{3/5}\right )-x^2} \, dx,x,2 (-1)^{3/10}-2 \sqrt [10]{-1} \tanh \left (\frac {x}{2}\right )\right )\\ &=-\frac {2 \sqrt [10]{-1} \tan ^{-1}\left (\frac {i+\sqrt [10]{-1} \tanh \left (\frac {x}{2}\right )}{\sqrt {1-\sqrt [5]{-1}}}\right )}{5 \sqrt {1-\sqrt [5]{-1}}}-\frac {2 \tanh ^{-1}\left (\frac {(-1)^{3/5}-\tanh \left (\frac {x}{2}\right )}{\sqrt {1-\sqrt [5]{-1}}}\right )}{5 \sqrt {1-\sqrt [5]{-1}}}+\frac {1}{5} \sqrt {2} \tanh ^{-1}\left (\frac {1+\tanh \left (\frac {x}{2}\right )}{\sqrt {2}}\right )+\frac {2 \tanh ^{-1}\left (\frac {(-1)^{4/5}+\tanh \left (\frac {x}{2}\right )}{\sqrt {1-(-1)^{3/5}}}\right )}{5 \sqrt {1-(-1)^{3/5}}}-\frac {2 \sqrt [10]{-1} \tanh ^{-1}\left (\frac {(-1)^{3/10}-\sqrt [10]{-1} \tanh \left (\frac {x}{2}\right )}{\sqrt {\sqrt [5]{-1}+(-1)^{3/5}}}\right )}{5 \sqrt {\sqrt [5]{-1}+(-1)^{3/5}}}\\ \end {align*}
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Mathematica [C] time = 0.95, size = 437, normalized size = 1.92 \[ \frac {1}{10} \left (\text {RootSum}\left [\text {$\#$1}^8+2 \text {$\#$1}^7+2 \text {$\#$1}^5+14 \text {$\#$1}^4-2 \text {$\#$1}^3-2 \text {$\#$1}+1\& ,\frac {\text {$\#$1}^6 x+2 \text {$\#$1}^6 \log \left (-\text {$\#$1} \sinh \left (\frac {x}{2}\right )+\text {$\#$1} \cosh \left (\frac {x}{2}\right )-\sinh \left (\frac {x}{2}\right )-\cosh \left (\frac {x}{2}\right )\right )+4 \text {$\#$1}^5 x+8 \text {$\#$1}^5 \log \left (-\text {$\#$1} \sinh \left (\frac {x}{2}\right )+\text {$\#$1} \cosh \left (\frac {x}{2}\right )-\sinh \left (\frac {x}{2}\right )-\cosh \left (\frac {x}{2}\right )\right )+9 \text {$\#$1}^4 x+18 \text {$\#$1}^4 \log \left (-\text {$\#$1} \sinh \left (\frac {x}{2}\right )+\text {$\#$1} \cosh \left (\frac {x}{2}\right )-\sinh \left (\frac {x}{2}\right )-\cosh \left (\frac {x}{2}\right )\right )+24 \text {$\#$1}^3 x+48 \text {$\#$1}^3 \log \left (-\text {$\#$1} \sinh \left (\frac {x}{2}\right )+\text {$\#$1} \cosh \left (\frac {x}{2}\right )-\sinh \left (\frac {x}{2}\right )-\cosh \left (\frac {x}{2}\right )\right )-9 \text {$\#$1}^2 x-18 \text {$\#$1}^2 \log \left (-\text {$\#$1} \sinh \left (\frac {x}{2}\right )+\text {$\#$1} \cosh \left (\frac {x}{2}\right )-\sinh \left (\frac {x}{2}\right )-\cosh \left (\frac {x}{2}\right )\right )+4 \text {$\#$1} x+8 \text {$\#$1} \log \left (-\text {$\#$1} \sinh \left (\frac {x}{2}\right )+\text {$\#$1} \cosh \left (\frac {x}{2}\right )-\sinh \left (\frac {x}{2}\right )-\cosh \left (\frac {x}{2}\right )\right )-2 \log \left (-\text {$\#$1} \sinh \left (\frac {x}{2}\right )+\text {$\#$1} \cosh \left (\frac {x}{2}\right )-\sinh \left (\frac {x}{2}\right )-\cosh \left (\frac {x}{2}\right )\right )-x}{4 \text {$\#$1}^7+7 \text {$\#$1}^6+5 \text {$\#$1}^4+28 \text {$\#$1}^3-3 \text {$\#$1}^2-1}\& \right ]+2 \sqrt {2} \tanh ^{-1}\left (\frac {\tanh \left (\frac {x}{2}\right )+1}{\sqrt {2}}\right )\right ) \]
Antiderivative was successfully verified.
[In]
Integrate[(1 - Sinh[x]^5)^(-1),x]
[Out]
(2*Sqrt[2]*ArcTanh[(1 + Tanh[x/2])/Sqrt[2]] + RootSum[1 - 2*#1 - 2*#1^3 + 14*#1^4 + 2*#1^5 + 2*#1^7 + #1^8 & ,
(-x - 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1] + 4*x*#1 + 8*Log[-Cosh[x/2] - Sinh[x/2] + C
osh[x/2]*#1 - Sinh[x/2]*#1]*#1 - 9*x*#1^2 - 18*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^2
+ 24*x*#1^3 + 48*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^3 + 9*x*#1^4 + 18*Log[-Cosh[x/2]
- Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^4 + 4*x*#1^5 + 8*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Si
nh[x/2]*#1]*#1^5 + x*#1^6 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^6)/(-1 - 3*#1^2 + 2
8*#1^3 + 5*#1^4 + 7*#1^6 + 4*#1^7) & ])/10
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fricas [B] time = 2.65, size = 3500, normalized size = 15.35 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-sinh(x)^5),x, algorithm="fricas")
[Out]
1/200*sqrt(2)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*(3*sqr
t(5) - 5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3)*arctan(1/40*sqrt(2)*((11*sqrt(5) - 25)*e^x + 7*sqrt(5) - 15)*s
qrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 1/80*sqrt(2)*(sqrt(2)*((11*sqrt(5) - 25)*e^x - 4*sqrt(5) + 10)*sqrt(2*s
qrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((3*sqrt(5) - 5)*e^x - 7*sqrt(5) + 15)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 3
) + 1/12800*(80*sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 40*sqrt(2)*(sqrt(2)*(5*sqrt(5
) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 3))*sqrt(sqrt(5) + 3) + sqrt(
2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*(7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*s
qrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*(17*sqrt(5) -
35)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) +
320*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 4))*sqrt(-20*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) - 40*(sqrt(5) - 1)*e^
x + 2*(sqrt(2)*((2*sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*
sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 80*e^(2*x) + 80) +
1/640*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*((3*sqrt(5) - 7)*e^x - 8*s
qrt(5) + 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x - 2*sqrt(5) + 4)*sqrt(2*sqrt(5) +
5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*((7*sqrt(5) - 17)*e^x - 8*sqrt(5) + 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt
(5) + 3) + 2*((5*sqrt(5) - 11)*e^x - 5*sqrt(5) + 9)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) + 1/20*(2*(4*
sqrt(5) - 5)*e^x + sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)) + 1/200*sqrt(2)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(
5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*(3*sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3)*arctan(
-1/40*sqrt(2)*((11*sqrt(5) - 25)*e^x + 7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) - 1/80*sqrt(2)*(s
qrt(2)*((11*sqrt(5) - 25)*e^x - 4*sqrt(5) + 10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((3*sqrt(5) - 5)*e^x
- 7*sqrt(5) + 15)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 3) - 1/12800*(80*sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5
) + 5)*sqrt(sqrt(5) + 3) + 40*sqrt(2)*(sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*sqrt
(2*sqrt(5) + 5)*(sqrt(5) - 3))*sqrt(sqrt(5) + 3) - sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5
) + 20)*((sqrt(2)*(7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5)
+ 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*(17*sqrt(5) - 35)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt
(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) + 320*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 4))*sqrt(-20*sqrt(
2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) - 40*(sqrt(5) - 1)*e^x - 2*(sqrt(2)*((2*sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*s
qrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*s
qrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 80*e^(2*x) + 80) + 1/640*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3
) - 4*sqrt(5) + 20)*((sqrt(2)*((3*sqrt(5) - 7)*e^x - 8*sqrt(5) + 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2
*((5*sqrt(5) - 11)*e^x - 2*sqrt(5) + 4)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*((7*sqrt(5) -
17)*e^x - 8*sqrt(5) + 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x - 5*sqrt(5) + 9)*sq
rt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) - 1/20*(2*(4*sqrt(5) - 5)*e^x + sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)) -
1/400*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(3*sqrt(5) + 5)*sqrt(-2*sqrt(5) + 5)*(-8*
sqrt(5) + 24)^(3/4)*arctan(-1/1280*((4*(5*sqrt(5) + 11)*e^x + ((3*sqrt(5) + 7)*e^x - 8*sqrt(5) - 18)*sqrt(-8*s
qrt(5) + 24) - 8*sqrt(5) - 16)*(-8*sqrt(5) + 24)^(3/4) + 4*(4*(5*sqrt(5) + 11)*e^x + ((7*sqrt(5) + 17)*e^x - 8
*sqrt(5) - 18)*sqrt(-8*sqrt(5) + 24) - 20*sqrt(5) - 36)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8
*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 1/25600*((((7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + 44
*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(3/4) + 4*((17*sqrt(5) + 35)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*s
qrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) - 20*((
(5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 12)*sqrt(-8*sqrt(5) + 24) + 4*(5*sqrt(5) + 11)*sqrt(-8*sq
rt(5) + 24) + 32*sqrt(5) + 128)*sqrt(-2*sqrt(5) + 5))*sqrt(40*(sqrt(5) + 1)*e^x + (4*(sqrt(5) + 5)*e^x + ((2*s
qrt(5) + 5)*e^x + 3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 6*sqrt(5) + 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5)
+ 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 10*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 80*e^(2*x) + 80) +
1/320*(32*(4*sqrt(5) + 5)*e^x + 4*((11*sqrt(5) + 25)*e^x + 7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + (4*(3*sqrt
(5) + 5)*e^x + ((11*sqrt(5) + 25)*e^x - 4*sqrt(5) - 10)*sqrt(-8*sqrt(5) + 24) - 28*sqrt(5) - 60)*sqrt(-8*sqrt(
5) + 24) + 16*sqrt(5) + 80)*sqrt(-2*sqrt(5) + 5)) - 1/400*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt
(5) + 20)*(3*sqrt(5) + 5)*sqrt(-2*sqrt(5) + 5)*(-8*sqrt(5) + 24)^(3/4)*arctan(-1/1280*((4*(5*sqrt(5) + 11)*e^x
+ ((3*sqrt(5) + 7)*e^x - 8*sqrt(5) - 18)*sqrt(-8*sqrt(5) + 24) - 8*sqrt(5) - 16)*(-8*sqrt(5) + 24)^(3/4) + 4*
(4*(5*sqrt(5) + 11)*e^x + ((7*sqrt(5) + 17)*e^x - 8*sqrt(5) - 18)*sqrt(-8*sqrt(5) + 24) - 20*sqrt(5) - 36)*(-8
*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 1/2
5600*((((7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(3/4) + 4*((17*sqrt(5) +
35)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) +
24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 20*(((5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 12)*sq
rt(-8*sqrt(5) + 24) + 4*(5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 32*sqrt(5) + 128)*sqrt(-2*sqrt(5) + 5))*sqrt(
40*(sqrt(5) + 1)*e^x - (4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x + 3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 6*
sqrt(5) + 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 10*(sqrt
(5) + 3)*sqrt(-8*sqrt(5) + 24) + 80*e^(2*x) + 80) - 1/320*(32*(4*sqrt(5) + 5)*e^x + 4*((11*sqrt(5) + 25)*e^x +
7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + (4*(3*sqrt(5) + 5)*e^x + ((11*sqrt(5) + 25)*e^x - 4*sqrt(5) - 10)*sqr
t(-8*sqrt(5) + 24) - 28*sqrt(5) - 60)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5) + 80)*sqrt(-2*sqrt(5) + 5)) - 1/800*(
sqrt(2)*(3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 8*sqrt(5))*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sq
rt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*log(-4*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) - 8*(sqrt(5) - 1)*e^x + 2/5*
(sqrt(2)*((2*sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(2
*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 16*e^(2*x) + 16) + 1/800
*(sqrt(2)*(3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 8*sqrt(5))*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*
sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*log(-4*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) - 8*(sqrt(5) - 1)*e^x - 2/
5*(sqrt(2)*((2*sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt
(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 16*e^(2*x) + 16) - 1/1
600*((3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(
5) + 20)*(-8*sqrt(5) + 24)^(1/4)*log(8*(sqrt(5) + 1)*e^x + 1/5*(4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x + 3
*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 6*sqrt(5) + 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5)
+ 20)*(-8*sqrt(5) + 24)^(1/4) + 2*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 16*e^(2*x) + 16) + 1/1600*((3*sqrt(5)
+ 5)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqr
t(5) + 24)^(1/4)*log(8*(sqrt(5) + 1)*e^x - 1/5*(4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x + 3*sqrt(5) + 5)*sq
rt(-8*sqrt(5) + 24) + 6*sqrt(5) + 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5
) + 24)^(1/4) + 2*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 16*e^(2*x) + 16) + 1/10*sqrt(2)*log((2*(sqrt(2) - 1)*e
^x - 2*sqrt(2) + e^(2*x) + 3)/(e^(2*x) - 2*e^x - 1))
________________________________________________________________________________________
giac [B] time = 2.95, size = 5248, normalized size = 23.02 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-sinh(x)^5),x, algorithm="giac")
[Out]
8/25*5^(3/4)*sqrt(-1/32*sqrt(5) + 5/64)*arctan(-2*(4789310072875935951200*5^(3/4)*sqrt(-2*sqrt(5) + 5) - 17997
45554293062228687680*sqrt(5)*sqrt(-2*sqrt(5) + 5) - 325914041979902244813289*5^(3/4) - 10520606548600849190560
*5^(1/4)*sqrt(-2*sqrt(5) + 5) + 265033340677886980055183*sqrt(5) + 4025305730691667696322880*sqrt(-2*sqrt(5) +
5) + 728855245658450343948919*5^(1/4) + 1637333558120632636*e^x - 592460559708252630357201)/(9202754427496321
314406*5^(3/4)*sqrt(-2*sqrt(5) + 5) + 1038239983143393667165790*sqrt(5)*sqrt(-2*sqrt(5) + 5) + 186591807316241
026405751*5^(3/4) - 20768219695320392550210*5^(1/4)*sqrt(-2*sqrt(5) + 5) + 576155331981489353033147*sqrt(5) -
2322370119525925506249090*sqrt(-2*sqrt(5) + 5) - 417362544266571988465273*5^(1/4) - 1288784580381451028672113)
) - 8/25*5^(3/4)*sqrt(-1/32*sqrt(5) + 5/64)*arctan(-2*(4315023771046590689440*5^(3/4)*sqrt(-2*sqrt(5) + 5) + 1
6512422419052472973244480*sqrt(5)*sqrt(-2*sqrt(5) + 5) + 2991559181950156635096041*5^(3/4) - 11415488961128059
998560*5^(1/4)*sqrt(-2*sqrt(5) + 5) + 476470546695231758102799*sqrt(5) - 36931036359499378163241280*sqrt(-2*sq
rt(5) + 5) - 6690300251147369625285239*5^(1/4) + 1637333558120632636*e^x - 1067630744269504182665681)/(5376890
66142690749994*5^(3/4)*sqrt(-2*sqrt(5) + 5) + 45162997328032147105966190*sqrt(5)*sqrt(-2*sqrt(5) + 5) + 818625
7622186710975158757*5^(3/4) - 5838120100393683185390*5^(1/4)*sqrt(-2*sqrt(5) + 5) + 603739022767920301057079*s
qrt(5) - 101008886798639244060001970*sqrt(-2*sqrt(5) + 5) - 18307539608818658210592747*5^(1/4) - 1355343042548
851351155477)) - 1/10*sqrt(sqrt(5) + 2)*log((302427386195713850867712*sqrt(5)*(2*sqrt(5) + 5)^3 + 172815649254
693629067264*(2*sqrt(5) + 5)^(7/2) + 226820539646785388150784*sqrt(5)*(2*sqrt(5) + 5)^(5/2)*sqrt(sqrt(5) + 2)
+ 151213693097856925433856*(2*sqrt(5) + 5)^3*sqrt(sqrt(5) + 2) + 70881418639620433797120*sqrt(5)*(2*sqrt(5) +
5)^2*(sqrt(5) + 2) + 56705134911696347037696*(2*sqrt(5) + 5)^(5/2)*(sqrt(5) + 2) + 11813569773270072299520*sqr
t(5)*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^(3/2) + 11813569773270072299520*(2*sqrt(5) + 5)^2*(sqrt(5) + 2)^(3/2)
+ 1107522166244069278080*sqrt(5)*(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 + 1476696221658759037440*(2*sqrt(5) + 5)^(3/
2)*(sqrt(5) + 2)^2 + 55376108312203463904*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) + 110752216624406927
808*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) + 1153668923170905498*sqrt(5)*(sqrt(5) + 2)^3 + 4614675692683621992*sq
rt(2*sqrt(5) + 5)*(sqrt(5) + 2)^3 + 82404923083636107*(sqrt(5) + 2)^(7/2) - 622619531678741564620800*sqrt(5)*(
2*sqrt(5) + 5)^(5/2) - 415079687785827709747200*(2*sqrt(5) + 5)^3 - 389137207299213477888000*sqrt(5)*(2*sqrt(5
) + 5)^2*sqrt(sqrt(5) + 2) - 311309765839370782310400*(2*sqrt(5) + 5)^(5/2)*sqrt(sqrt(5) + 2) - 97284301824803
369472000*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2) - 97284301824803369472000*(2*sqrt(5) + 5)^2*(sqrt(5) + 2
) - 12160537728100421184000*sqrt(5)*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 16214050304133894912000*(2*sqrt(5) +
5)^(3/2)*(sqrt(5) + 2)^(3/2) - 760033608006276324000*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 1520067216
012552648000*(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 19000840200156908100*sqrt(5)*(sqrt(5) + 2)^(5/2) - 760033608006
27632400*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) - 1583403350013075675*(sqrt(5) + 2)^3 - 346430300390652274610
1760*sqrt(5)*(2*sqrt(5) + 5)^2 - 2015373937635933569712128*(2*sqrt(5) + 5)^(5/2) - 1732151501953261373050880*s
qrt(5)*(2*sqrt(5) + 5)^(3/2)*sqrt(sqrt(5) + 2) - 1259608711022458481070080*(2*sqrt(5) + 5)^2*sqrt(sqrt(5) + 2)
- 324778406616236507447040*sqrt(5)*(2*sqrt(5) + 5)*(sqrt(5) + 2) - 314902177755614620267520*(2*sqrt(5) + 5)^(
3/2)*(sqrt(5) + 2) - 27064867218019708953920*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 393627722194518
27533440*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 845777100563115904810*sqrt(5)*(sqrt(5) + 2)^2 - 246017326371573
9220840*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 61504331592893480521*(sqrt(5) + 2)^(5/2) + 395970371725009869321
4208*sqrt(5)*(2*sqrt(5) + 5)^(3/2) + 2662579692919387100254208*(2*sqrt(5) + 5)^2 + 1484888893968787009955328*s
qrt(5)*(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 1331289846459693550127104*(2*sqrt(5) + 5)^(3/2)*sqrt(sqrt(5) + 2) +
185611111746098376244416*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2) + 249616846211192540648832*(2*sqrt(5) + 5)
*(sqrt(5) + 2) + 7733796322754099010184*sqrt(5)*(sqrt(5) + 2)^(3/2) + 20801403850932711720736*sqrt(2*sqrt(5) +
5)*(sqrt(5) + 2)^(3/2) + 650043870341647241273*(sqrt(5) + 2)^2 + 10991940456909382283282816*sqrt(5)*(2*sqrt(5
) + 5) + 8567053742081103206220288*(2*sqrt(5) + 5)^(3/2) + 2747985114227345570820704*sqrt(5)*sqrt(2*sqrt(5) +
5)*sqrt(sqrt(5) + 2) + 3212645153280413702332608*(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 171749069639209098176294*
sqrt(5)*(sqrt(5) + 2) + 401580644160051712791576*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2) + 16732526840002154699649*(
sqrt(5) + 2)^(3/2) - 2557269775899525489493536*sqrt(5)*sqrt(2*sqrt(5) + 5) - 319658721987440686186692*sqrt(5)*
sqrt(sqrt(5) + 2) + 39842775211562571442672*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) - 3308326863346966249269767*
sqrt(5) - 4580301686563984868886360*sqrt(2*sqrt(5) + 5) - 572537710820498108610795*sqrt(sqrt(5) + 2) + 2850824
269841065226382633)^2 + 64*(24322822501240781930496*sqrt(5)*(2*sqrt(5) + 5)^3 + 13898755714994732531712*(2*sqr
t(5) + 5)^(7/2) + 18242116875930586447872*sqrt(5)*(2*sqrt(5) + 5)^(5/2)*sqrt(sqrt(5) + 2) + 121614112506203909
65248*(2*sqrt(5) + 5)^3*sqrt(sqrt(5) + 2) + 5700661523728308264960*sqrt(5)*(2*sqrt(5) + 5)^2*(sqrt(5) + 2) + 4
560529218982646611968*(2*sqrt(5) + 5)^(5/2)*(sqrt(5) + 2) + 950110253954718044160*sqrt(5)*(2*sqrt(5) + 5)^(3/2
)*(sqrt(5) + 2)^(3/2) + 950110253954718044160*(2*sqrt(5) + 5)^2*(sqrt(5) + 2)^(3/2) + 89072836308254816640*sqr
t(5)*(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 + 118763781744339755520*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^2 + 445364181
5412740832*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) + 8907283630825481664*(2*sqrt(5) + 5)*(sqrt(5) + 2)
^(5/2) + 92784204487765434*sqrt(5)*(sqrt(5) + 2)^3 + 371136817951061736*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^3 +
6627443177697531*(sqrt(5) + 2)^(7/2) - 13726081827177108602880*sqrt(5)*(2*sqrt(5) + 5)^(5/2) - 915072121811807
2401920*(2*sqrt(5) + 5)^3 - 8578801141985692876800*sqrt(5)*(2*sqrt(5) + 5)^2*sqrt(sqrt(5) + 2) - 6863040913588
554301440*(2*sqrt(5) + 5)^(5/2)*sqrt(sqrt(5) + 2) - 2144700285496423219200*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*(sqrt
(5) + 2) - 2144700285496423219200*(2*sqrt(5) + 5)^2*(sqrt(5) + 2) - 268087535687052902400*sqrt(5)*(2*sqrt(5) +
5)*(sqrt(5) + 2)^(3/2) - 357450047582737203200*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^(3/2) - 167554709804408064
00*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 33510941960881612800*(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 418886
774511020160*sqrt(5)*(sqrt(5) + 2)^(5/2) - 1675547098044080640*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) - 34907
231209251680*(sqrt(5) + 2)^3 - 323167802334835240755200*sqrt(5)*(2*sqrt(5) + 5)^2 - 197727185614766237777920*(
2*sqrt(5) + 5)^(5/2) - 161583901167417620377600*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*sqrt(sqrt(5) + 2) - 123579491009
228898611200*(2*sqrt(5) + 5)^2*sqrt(sqrt(5) + 2) - 30296981468890803820800*sqrt(5)*(2*sqrt(5) + 5)*(sqrt(5) +
2) - 30894872752307224652800*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2) - 2524748455740900318400*sqrt(5)*sqrt(2*sqrt(
5) + 5)*(sqrt(5) + 2)^(3/2) - 3861859094038403081600*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 7889838924190313495
0*sqrt(5)*(sqrt(5) + 2)^2 - 241366193377400192600*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 6034154834435004815*(s
qrt(5) + 2)^(5/2) - 100890523270644033265664*sqrt(5)*(2*sqrt(5) + 5)^(3/2) - 129486527077263009521664*(2*sqrt(
5) + 5)^2 - 37833946226491512474624*sqrt(5)*(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) - 64743263538631504760832*(2*sqr
t(5) + 5)^(3/2)*sqrt(sqrt(5) + 2) - 4729243278311439059328*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2) - 1213936
1913493407142656*(2*sqrt(5) + 5)*(sqrt(5) + 2) - 197051803262976627472*sqrt(5)*(sqrt(5) + 2)^(3/2) - 101161349
2791117261888*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 31612921649722414434*(sqrt(5) + 2)^2 + 976056667738889
843134336*sqrt(5)*(2*sqrt(5) + 5) + 737459612988335241742848*(2*sqrt(5) + 5)^(3/2) + 244014166934722460783584*
sqrt(5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 276547354870625715653568*(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 1
5250885433420153798974*sqrt(5)*(sqrt(5) + 2) + 34568419358828214456696*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2) + 144
0350806617842269029*(sqrt(5) + 2)^(3/2) + 865777074090951821677952*sqrt(5)*sqrt(2*sqrt(5) + 5) + 1082221342613
68977709744*sqrt(5)*sqrt(sqrt(5) + 2) + 403147498761313336459456*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 33990
14754330436228284234*sqrt(5) + 1479783698747530204584760*sqrt(2*sqrt(5) + 5) + 184972962343441275573095*sqrt(s
qrt(5) + 2) + 131291208062174938773104*e^x + 8700694617036282266881102)^2) + 1/10*sqrt(sqrt(5) + 2)*log((29677
7725783310857666560*sqrt(5)*(2*sqrt(5) + 5)^3 + 169587271876177632952320*(2*sqrt(5) + 5)^(7/2) + 2225832943374
83143249920*sqrt(5)*(2*sqrt(5) + 5)^(5/2)*sqrt(sqrt(5) + 2) + 148388862891655428833280*(2*sqrt(5) + 5)^3*sqrt(
sqrt(5) + 2) + 69557279480463482265600*sqrt(5)*(2*sqrt(5) + 5)^2*(sqrt(5) + 2) + 55645823584370785812480*(2*sq
rt(5) + 5)^(5/2)*(sqrt(5) + 2) + 11592879913410580377600*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^(3/2) + 1
1592879913410580377600*(2*sqrt(5) + 5)^2*(sqrt(5) + 2)^(3/2) + 1086832491882241910400*sqrt(5)*(2*sqrt(5) + 5)*
(sqrt(5) + 2)^2 + 1449109989176322547200*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^2 + 54341624594112095520*sqrt(5)*
sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) + 108683249188224191040*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) + 11321171
79044001990*sqrt(5)*(sqrt(5) + 2)^3 + 4528468716176007960*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^3 + 80865512788857
285*(sqrt(5) + 2)^(7/2) - 562345414061023649464320*sqrt(5)*(2*sqrt(5) + 5)^(5/2) - 374896942707349099642880*(2
*sqrt(5) + 5)^3 - 351465883788139780915200*sqrt(5)*(2*sqrt(5) + 5)^2*sqrt(sqrt(5) + 2) - 281172707030511824732
160*(2*sqrt(5) + 5)^(5/2)*sqrt(sqrt(5) + 2) - 87866470947034945228800*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) +
2) - 87866470947034945228800*(2*sqrt(5) + 5)^2*(sqrt(5) + 2) - 10983308868379368153600*sqrt(5)*(2*sqrt(5) + 5
)*(sqrt(5) + 2)^(3/2) - 14644411824505824204800*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^(3/2) - 686456804273710509
600*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 1372913608547421019200*(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 171
61420106842762740*sqrt(5)*(sqrt(5) + 2)^(5/2) - 68645680427371050960*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) -
1430118342236896895*(sqrt(5) + 2)^3 - 3521311589437476455997440*sqrt(5)*(2*sqrt(5) + 5)^2 - 20751049570917040
20631552*(2*sqrt(5) + 5)^(5/2) - 1760655794718738227998720*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*sqrt(sqrt(5) + 2) - 1
296940598182315012894720*(2*sqrt(5) + 5)^2*sqrt(sqrt(5) + 2) - 330122961509763417749760*sqrt(5)*(2*sqrt(5) + 5
)*(sqrt(5) + 2) - 324235149545578753223680*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2) - 27510246792480284812480*sqrt(
5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 40529393693197344152960*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 859
695212265008900390*sqrt(5)*(sqrt(5) + 2)^2 - 2533087105824834009560*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 6332
7177645620850239*(sqrt(5) + 2)^(5/2) + 3427066584376513776799744*sqrt(5)*(2*sqrt(5) + 5)^(3/2) + 2255513638416
047840415744*(2*sqrt(5) + 5)^2 + 1285149969141192666299904*sqrt(5)*(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 1127756
819208023920207872*(2*sqrt(5) + 5)^(3/2)*sqrt(sqrt(5) + 2) + 160643746142649083287488*sqrt(5)*sqrt(2*sqrt(5) +
5)*(sqrt(5) + 2) + 211454403601504485038976*(2*sqrt(5) + 5)*(sqrt(5) + 2) + 6693489422610378470312*sqrt(5)*(s
qrt(5) + 2)^(3/2) + 17621200300125373753248*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) + 550662509378917929789*(s
qrt(5) + 2)^2 + 11519381554046905848481408*sqrt(5)*(2*sqrt(5) + 5) + 9181179291975798227910144*(2*sqrt(5) + 5)
^(3/2) + 2879845388511726462120352*sqrt(5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 3442942234490924335466304*(
2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 179990336781982903882522*sqrt(5)*(sqrt(5) + 2) + 430367779311365541933288*s
qrt(2*sqrt(5) + 5)*(sqrt(5) + 2) + 17931990804640230913887*(sqrt(5) + 2)^(3/2) - 1493985186915806421972384*sqr
t(5)*sqrt(2*sqrt(5) + 5) - 186748148364475802746548*sqrt(5)*sqrt(sqrt(5) + 2) + 397187773282286465287728*sqrt(
2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) - 590811650205465011212999*sqrt(5) - 4784256889606509508420584*sqrt(2*sqrt(5)
+ 5) - 598032111200813688552573*sqrt(sqrt(5) + 2) + 9613265583240077072561069)^2 + 64*(2809473664752684367872
0*sqrt(5)*(2*sqrt(5) + 5)^3 + 16054135227158196387840*(2*sqrt(5) + 5)^(7/2) + 21071052485645132759040*sqrt(5)*
(2*sqrt(5) + 5)^(5/2)*sqrt(sqrt(5) + 2) + 14047368323763421839360*(2*sqrt(5) + 5)^3*sqrt(sqrt(5) + 2) + 658470
3901764103987200*sqrt(5)*(2*sqrt(5) + 5)^2*(sqrt(5) + 2) + 5267763121411283189760*(2*sqrt(5) + 5)^(5/2)*(sqrt(
5) + 2) + 1097450650294017331200*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^(3/2) + 1097450650294017331200*(2
*sqrt(5) + 5)^2*(sqrt(5) + 2)^(3/2) + 102885998465064124800*sqrt(5)*(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 + 13718133
1286752166400*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^2 + 5144299923253206240*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5)
+ 2)^(5/2) + 10288599846506412480*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) + 107172915067775130*sqrt(5)*(sqrt(5) +
2)^3 + 428691660271100520*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^3 + 7655208219126795*(sqrt(5) + 2)^(7/2) - 207558
36954363830992896*sqrt(5)*(2*sqrt(5) + 5)^(5/2) - 13837224636242553995264*(2*sqrt(5) + 5)^3 - 1297239809647739
4370560*sqrt(5)*(2*sqrt(5) + 5)^2*sqrt(sqrt(5) + 2) - 10377918477181915496448*(2*sqrt(5) + 5)^(5/2)*sqrt(sqrt(
5) + 2) - 3243099524119348592640*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2) - 3243099524119348592640*(2*sqrt(
5) + 5)^2*(sqrt(5) + 2) - 405387440514918574080*sqrt(5)*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 5405165873532247
65440*(2*sqrt(5) + 5)^(3/2)*(sqrt(5) + 2)^(3/2) - 25336715032182410880*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) +
2)^2 - 50673430064364821760*(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 633417875804560272*sqrt(5)*(sqrt(5) + 2)^(5/2) -
2533671503218241088*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(5/2) - 52784822983713356*(sqrt(5) + 2)^3 - 36352828004
5460787978240*sqrt(5)*(2*sqrt(5) + 5)^2 - 220585782417551521185792*(2*sqrt(5) + 5)^(5/2) - 1817641400227303939
89120*sqrt(5)*(2*sqrt(5) + 5)^(3/2)*sqrt(sqrt(5) + 2) - 137866114010969700741120*(2*sqrt(5) + 5)^2*sqrt(sqrt(5
) + 2) - 34080776254261948872960*sqrt(5)*(2*sqrt(5) + 5)*(sqrt(5) + 2) - 34466528502742425185280*(2*sqrt(5) +
5)^(3/2)*(sqrt(5) + 2) - 2840064687855162406080*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 430831606284
2803148160*(2*sqrt(5) + 5)*(sqrt(5) + 2)^(3/2) - 88752021495473825190*sqrt(5)*(sqrt(5) + 2)^2 - 26926975392767
5196760*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2)^2 - 6731743848191879919*(sqrt(5) + 2)^(5/2) - 7036498169930170929152
0*sqrt(5)*(2*sqrt(5) + 5)^(3/2) - 113606308687559690526720*(2*sqrt(5) + 5)^2 - 26386868137238140984320*sqrt(5)
*(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) - 56803154343779845263360*(2*sqrt(5) + 5)^(3/2)*sqrt(sqrt(5) + 2) - 3298358
517154767623040*sqrt(5)*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2) - 10650591439458720986880*(2*sqrt(5) + 5)*(sqrt(5) +
2) - 137431604881448650960*sqrt(5)*(sqrt(5) + 2)^(3/2) - 887549286621560082240*sqrt(2*sqrt(5) + 5)*(sqrt(5) +
2)^(3/2) - 27735915206923752570*(sqrt(5) + 2)^2 + 1084940669680612606048128*sqrt(5)*(2*sqrt(5) + 5) + 8114417
42157208365935104*(2*sqrt(5) + 5)^(3/2) + 271235167420153151512032*sqrt(5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) +
2) + 304290653308953137225664*(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 16952197963759571969502*sqrt(5)*(sqrt(5) + 2
) + 38036331663619142153208*sqrt(2*sqrt(5) + 5)*(sqrt(5) + 2) + 1584847152650797589717*(sqrt(5) + 2)^(3/2) + 9
16330240481116591230464*sqrt(5)*sqrt(2*sqrt(5) + 5) + 114541280060139573903808*sqrt(5)*sqrt(sqrt(5) + 2) + 438
878646396292635288832*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 2) + 3690050822522820384588494*sqrt(5) + 159144518236
5082778211384*sqrt(2*sqrt(5) + 5) + 198930647795635347276423*sqrt(sqrt(5) + 2) - 131291208062174938773104*e^x
+ 9240055035301648563405942)^2) - 1/10*sqrt(2)*log(abs(-2*sqrt(2) + 2*e^x - 2)/abs(2*sqrt(2) + 2*e^x - 2)) - 1
/10*5^(1/4)*log(6400*(9202754427496321314406*5^(3/4)*sqrt(-2*sqrt(5) + 5) + 1038239983143393667165790*sqrt(5)*
sqrt(-2*sqrt(5) + 5) + 186591807316241026405751*5^(3/4) - 20768219695320392550210*5^(1/4)*sqrt(-2*sqrt(5) + 5)
+ 576155331981489353033147*sqrt(5) - 2322370119525925506249090*sqrt(-2*sqrt(5) + 5) - 41736254426657198846527
3*5^(1/4) - 1288784580381451028672113)^2 + 25600*(4789310072875935951200*5^(3/4)*sqrt(-2*sqrt(5) + 5) - 179974
5554293062228687680*sqrt(5)*sqrt(-2*sqrt(5) + 5) - 325914041979902244813289*5^(3/4) - 10520606548600849190560*
5^(1/4)*sqrt(-2*sqrt(5) + 5) + 265033340677886980055183*sqrt(5) + 4025305730691667696322880*sqrt(-2*sqrt(5) +
5) + 728855245658450343948919*5^(1/4) + 1637333558120632636*e^x - 592460559708252630357201)^2) + 1/10*5^(1/4)*
log(25600*(4315023771046590689440*5^(3/4)*sqrt(-2*sqrt(5) + 5) + 16512422419052472973244480*sqrt(5)*sqrt(-2*sq
rt(5) + 5) + 2991559181950156635096041*5^(3/4) - 11415488961128059998560*5^(1/4)*sqrt(-2*sqrt(5) + 5) + 476470
546695231758102799*sqrt(5) - 36931036359499378163241280*sqrt(-2*sqrt(5) + 5) - 6690300251147369625285239*5^(1/
4) + 1637333558120632636*e^x - 1067630744269504182665681)^2 + 6400*(537689066142690749994*5^(3/4)*sqrt(-2*sqrt
(5) + 5) + 45162997328032147105966190*sqrt(5)*sqrt(-2*sqrt(5) + 5) + 8186257622186710975158757*5^(3/4) - 58381
20100393683185390*5^(1/4)*sqrt(-2*sqrt(5) + 5) + 603739022767920301057079*sqrt(5) - 10100888679863924406000197
0*sqrt(-2*sqrt(5) + 5) - 18307539608818658210592747*5^(1/4) - 1355343042548851351155477)^2) + 1/5*sqrt(2*sqrt(
5) + 5)*arctan((110641272*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^7 - 475726088*(2*sqrt(5) + sqr
t(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^6 - 10105915139*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^5
+ 16180495104*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^4 + 284235586966*(2*sqrt(5) + sqrt(2*sqrt(
5) + 5) + sqrt(sqrt(5) + 2))^3 - 13398309260*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^2 - 4747850
205816*sqrt(5) - 2373925102908*sqrt(2*sqrt(5) + 5) - 2373925102908*sqrt(sqrt(5) + 2) + 759635933456*e^x - 1242
609575248)/(256556994*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^7 - 892031217*(2*sqrt(5) + sqrt(2*
sqrt(5) + 5) + sqrt(sqrt(5) + 2))^6 - 25195966133*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^5 + 28
952708158*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^4 + 709750301398*(2*sqrt(5) + sqrt(2*sqrt(5) +
5) + sqrt(sqrt(5) + 2))^3 + 80692042496*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^2 - 11068354399
432*sqrt(5) - 5534177199716*sqrt(2*sqrt(5) + 5) - 5534177199716*sqrt(sqrt(5) + 2) - 3881375121088))/sqrt(sqrt(
5) + 2) - 1/5*sqrt(2*sqrt(5) + 5)*arctan((83633448*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^7 - 4
42112756*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^6 - 7188799155*(2*sqrt(5) + sqrt(2*sqrt(5) + 5)
+ sqrt(sqrt(5) + 2))^5 + 18979817940*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^4 + 194564340278*(
2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^3 - 178069044908*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(
sqrt(5) + 2))^2 - 2862929298552*sqrt(5) - 1431464649276*sqrt(2*sqrt(5) + 5) - 1431464649276*sqrt(sqrt(5) + 2)
- 759635933456*e^x - 101449315520)/(82684590*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^7 - 4169002
9*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^6 - 10052928883*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqr
t(sqrt(5) + 2))^5 - 3266507166*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^4 + 302724737258*(2*sqrt(
5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5) + 2))^3 + 148206122616*(2*sqrt(5) + sqrt(2*sqrt(5) + 5) + sqrt(sqrt(5)
+ 2))^2 - 4842785241848*sqrt(5) - 2421392620924*sqrt(2*sqrt(5) + 5) - 2421392620924*sqrt(sqrt(5) + 2) - 51107
7100176))/sqrt(sqrt(5) + 2)
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maple [C] time = 0.07, size = 124, normalized size = 0.54 \[ \frac {2 \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{8}-2 \textit {\_Z}^{7}-2 \textit {\_Z}^{5}+14 \textit {\_Z}^{4}+2 \textit {\_Z}^{3}+2 \textit {\_Z} +1\right )}{\sum }\frac {\left (-2 \textit {\_R}^{6}+3 \textit {\_R}^{5}+2 \textit {\_R}^{4}-2 \textit {\_R}^{3}-2 \textit {\_R}^{2}+3 \textit {\_R} +2\right ) \ln \left (\tanh \left (\frac {x}{2}\right )-\textit {\_R} \right )}{4 \textit {\_R}^{7}-7 \textit {\_R}^{6}-5 \textit {\_R}^{4}+28 \textit {\_R}^{3}+3 \textit {\_R}^{2}+1}\right )}{5}+\frac {\sqrt {2}\, \arctanh \left (\frac {\left (2 \tanh \left (\frac {x}{2}\right )+2\right ) \sqrt {2}}{4}\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(1-sinh(x)^5),x)
[Out]
2/5*sum((-2*_R^6+3*_R^5+2*_R^4-2*_R^3-2*_R^2+3*_R+2)/(4*_R^7-7*_R^6-5*_R^4+28*_R^3+3*_R^2+1)*ln(tanh(1/2*x)-_R
),_R=RootOf(_Z^8-2*_Z^7-2*_Z^5+14*_Z^4+2*_Z^3+2*_Z+1))+1/5*2^(1/2)*arctanh(1/4*(2*tanh(1/2*x)+2)*2^(1/2))
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {1}{10} \, \sqrt {2} \log \left (-\frac {\sqrt {2} - e^{x} + 1}{\sqrt {2} + e^{x} - 1}\right ) + \int \frac {2 \, {\left (e^{\left (7 \, x\right )} + 4 \, e^{\left (6 \, x\right )} + 9 \, e^{\left (5 \, x\right )} + 24 \, e^{\left (4 \, x\right )} - 9 \, e^{\left (3 \, x\right )} + 4 \, e^{\left (2 \, x\right )} - e^{x}\right )}}{5 \, {\left (e^{\left (8 \, x\right )} + 2 \, e^{\left (7 \, x\right )} + 2 \, e^{\left (5 \, x\right )} + 14 \, e^{\left (4 \, x\right )} - 2 \, e^{\left (3 \, x\right )} - 2 \, e^{x} + 1\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-sinh(x)^5),x, algorithm="maxima")
[Out]
-1/10*sqrt(2)*log(-(sqrt(2) - e^x + 1)/(sqrt(2) + e^x - 1)) + integrate(2/5*(e^(7*x) + 4*e^(6*x) + 9*e^(5*x) +
24*e^(4*x) - 9*e^(3*x) + 4*e^(2*x) - e^x)/(e^(8*x) + 2*e^(7*x) + 2*e^(5*x) + 14*e^(4*x) - 2*e^(3*x) - 2*e^x +
1), x)
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mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.00 \[ \text {Hanged} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-1/(sinh(x)^5 - 1),x)
[Out]
\text{Hanged}
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ - \int \frac {1}{\sinh ^{5}{\relax (x )} - 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(1-sinh(x)**5),x)
[Out]
-Integral(1/(sinh(x)**5 - 1), x)
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