Optimal. Leaf size=517 \[ -\frac {2 f^2 \sqrt {a^2+b^2} \text {Li}_3\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^3}+\frac {2 f^2 \sqrt {a^2+b^2} \text {Li}_3\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d^3}+\frac {2 f \sqrt {a^2+b^2} (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^2}-\frac {2 f \sqrt {a^2+b^2} (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d^2}+\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}+1\right )}{a^2 d}-\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (\frac {b e^{c+d x}}{\sqrt {a^2+b^2}+a}+1\right )}{a^2 d}-\frac {2 b f^2 \text {Li}_3\left (-e^{c+d x}\right )}{a^2 d^3}+\frac {2 b f^2 \text {Li}_3\left (e^{c+d x}\right )}{a^2 d^3}+\frac {2 b f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a^2 d^2}-\frac {2 b f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a^2 d^2}+\frac {2 b (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a^2 d}+\frac {f^2 \text {Li}_2\left (e^{2 (c+d x)}\right )}{a d^3}+\frac {2 f (e+f x) \log \left (1-e^{2 (c+d x)}\right )}{a d^2}-\frac {(e+f x)^2 \coth (c+d x)}{a d}-\frac {(e+f x)^2}{a d} \]
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Rubi [A] time = 1.30, antiderivative size = 517, normalized size of antiderivative = 1.00, number of steps used = 34, number of rules used = 18, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.643, Rules used = {5569, 3720, 3716, 2190, 2279, 2391, 32, 5585, 5450, 3296, 2638, 4182, 2531, 2282, 6589, 5565, 3322, 2264} \[ \frac {2 f \sqrt {a^2+b^2} (e+f x) \text {PolyLog}\left (2,-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^2}-\frac {2 f \sqrt {a^2+b^2} (e+f x) \text {PolyLog}\left (2,-\frac {b e^{c+d x}}{\sqrt {a^2+b^2}+a}\right )}{a^2 d^2}-\frac {2 f^2 \sqrt {a^2+b^2} \text {PolyLog}\left (3,-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^3}+\frac {2 f^2 \sqrt {a^2+b^2} \text {PolyLog}\left (3,-\frac {b e^{c+d x}}{\sqrt {a^2+b^2}+a}\right )}{a^2 d^3}+\frac {2 b f (e+f x) \text {PolyLog}\left (2,-e^{c+d x}\right )}{a^2 d^2}-\frac {2 b f (e+f x) \text {PolyLog}\left (2,e^{c+d x}\right )}{a^2 d^2}-\frac {2 b f^2 \text {PolyLog}\left (3,-e^{c+d x}\right )}{a^2 d^3}+\frac {2 b f^2 \text {PolyLog}\left (3,e^{c+d x}\right )}{a^2 d^3}+\frac {f^2 \text {PolyLog}\left (2,e^{2 (c+d x)}\right )}{a d^3}+\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}+1\right )}{a^2 d}-\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (\frac {b e^{c+d x}}{\sqrt {a^2+b^2}+a}+1\right )}{a^2 d}+\frac {2 b (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a^2 d}+\frac {2 f (e+f x) \log \left (1-e^{2 (c+d x)}\right )}{a d^2}-\frac {(e+f x)^2 \coth (c+d x)}{a d}-\frac {(e+f x)^2}{a d} \]
Antiderivative was successfully verified.
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Rule 32
Rule 2190
Rule 2264
Rule 2279
Rule 2282
Rule 2391
Rule 2531
Rule 2638
Rule 3296
Rule 3322
Rule 3716
Rule 3720
Rule 4182
Rule 5450
Rule 5565
Rule 5569
Rule 5585
Rule 6589
Rubi steps
\begin {align*} \int \frac {(e+f x)^2 \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx &=\frac {\int (e+f x)^2 \coth ^2(c+d x) \, dx}{a}-\frac {b \int \frac {(e+f x)^2 \cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx}{a}\\ &=-\frac {(e+f x)^2 \coth (c+d x)}{a d}+\frac {\int (e+f x)^2 \, dx}{a}-\frac {b \int (e+f x)^2 \cosh (c+d x) \coth (c+d x) \, dx}{a^2}+\frac {b^2 \int \frac {(e+f x)^2 \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx}{a^2}+\frac {(2 f) \int (e+f x) \coth (c+d x) \, dx}{a d}\\ &=-\frac {(e+f x)^2}{a d}+\frac {(e+f x)^3}{3 a f}-\frac {(e+f x)^2 \coth (c+d x)}{a d}-\frac {\int (e+f x)^2 \, dx}{a}-\frac {b \int (e+f x)^2 \text {csch}(c+d x) \, dx}{a^2}+\frac {\left (a^2+b^2\right ) \int \frac {(e+f x)^2}{a+b \sinh (c+d x)} \, dx}{a^2}-\frac {(4 f) \int \frac {e^{2 (c+d x)} (e+f x)}{1-e^{2 (c+d x)}} \, dx}{a d}\\ &=-\frac {(e+f x)^2}{a d}+\frac {2 b (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a^2 d}-\frac {(e+f x)^2 \coth (c+d x)}{a d}+\frac {2 f (e+f x) \log \left (1-e^{2 (c+d x)}\right )}{a d^2}+\frac {\left (2 \left (a^2+b^2\right )\right ) \int \frac {e^{c+d x} (e+f x)^2}{-b+2 a e^{c+d x}+b e^{2 (c+d x)}} \, dx}{a^2}+\frac {(2 b f) \int (e+f x) \log \left (1-e^{c+d x}\right ) \, dx}{a^2 d}-\frac {(2 b f) \int (e+f x) \log \left (1+e^{c+d x}\right ) \, dx}{a^2 d}-\frac {\left (2 f^2\right ) \int \log \left (1-e^{2 (c+d x)}\right ) \, dx}{a d^2}\\ &=-\frac {(e+f x)^2}{a d}+\frac {2 b (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a^2 d}-\frac {(e+f x)^2 \coth (c+d x)}{a d}+\frac {2 f (e+f x) \log \left (1-e^{2 (c+d x)}\right )}{a d^2}+\frac {2 b f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a^2 d^2}-\frac {2 b f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a^2 d^2}+\frac {\left (2 b \sqrt {a^2+b^2}\right ) \int \frac {e^{c+d x} (e+f x)^2}{2 a-2 \sqrt {a^2+b^2}+2 b e^{c+d x}} \, dx}{a^2}-\frac {\left (2 b \sqrt {a^2+b^2}\right ) \int \frac {e^{c+d x} (e+f x)^2}{2 a+2 \sqrt {a^2+b^2}+2 b e^{c+d x}} \, dx}{a^2}-\frac {f^2 \operatorname {Subst}\left (\int \frac {\log (1-x)}{x} \, dx,x,e^{2 (c+d x)}\right )}{a d^3}-\frac {\left (2 b f^2\right ) \int \text {Li}_2\left (-e^{c+d x}\right ) \, dx}{a^2 d^2}+\frac {\left (2 b f^2\right ) \int \text {Li}_2\left (e^{c+d x}\right ) \, dx}{a^2 d^2}\\ &=-\frac {(e+f x)^2}{a d}+\frac {2 b (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a^2 d}-\frac {(e+f x)^2 \coth (c+d x)}{a d}+\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d}-\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d}+\frac {2 f (e+f x) \log \left (1-e^{2 (c+d x)}\right )}{a d^2}+\frac {2 b f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a^2 d^2}-\frac {2 b f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a^2 d^2}+\frac {f^2 \text {Li}_2\left (e^{2 (c+d x)}\right )}{a d^3}-\frac {\left (2 \sqrt {a^2+b^2} f\right ) \int (e+f x) \log \left (1+\frac {2 b e^{c+d x}}{2 a-2 \sqrt {a^2+b^2}}\right ) \, dx}{a^2 d}+\frac {\left (2 \sqrt {a^2+b^2} f\right ) \int (e+f x) \log \left (1+\frac {2 b e^{c+d x}}{2 a+2 \sqrt {a^2+b^2}}\right ) \, dx}{a^2 d}-\frac {\left (2 b f^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2(-x)}{x} \, dx,x,e^{c+d x}\right )}{a^2 d^3}+\frac {\left (2 b f^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2(x)}{x} \, dx,x,e^{c+d x}\right )}{a^2 d^3}\\ &=-\frac {(e+f x)^2}{a d}+\frac {2 b (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a^2 d}-\frac {(e+f x)^2 \coth (c+d x)}{a d}+\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d}-\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d}+\frac {2 f (e+f x) \log \left (1-e^{2 (c+d x)}\right )}{a d^2}+\frac {2 b f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a^2 d^2}-\frac {2 b f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a^2 d^2}+\frac {2 \sqrt {a^2+b^2} f (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^2}-\frac {2 \sqrt {a^2+b^2} f (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d^2}+\frac {f^2 \text {Li}_2\left (e^{2 (c+d x)}\right )}{a d^3}-\frac {2 b f^2 \text {Li}_3\left (-e^{c+d x}\right )}{a^2 d^3}+\frac {2 b f^2 \text {Li}_3\left (e^{c+d x}\right )}{a^2 d^3}-\frac {\left (2 \sqrt {a^2+b^2} f^2\right ) \int \text {Li}_2\left (-\frac {2 b e^{c+d x}}{2 a-2 \sqrt {a^2+b^2}}\right ) \, dx}{a^2 d^2}+\frac {\left (2 \sqrt {a^2+b^2} f^2\right ) \int \text {Li}_2\left (-\frac {2 b e^{c+d x}}{2 a+2 \sqrt {a^2+b^2}}\right ) \, dx}{a^2 d^2}\\ &=-\frac {(e+f x)^2}{a d}+\frac {2 b (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a^2 d}-\frac {(e+f x)^2 \coth (c+d x)}{a d}+\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d}-\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d}+\frac {2 f (e+f x) \log \left (1-e^{2 (c+d x)}\right )}{a d^2}+\frac {2 b f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a^2 d^2}-\frac {2 b f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a^2 d^2}+\frac {2 \sqrt {a^2+b^2} f (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^2}-\frac {2 \sqrt {a^2+b^2} f (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d^2}+\frac {f^2 \text {Li}_2\left (e^{2 (c+d x)}\right )}{a d^3}-\frac {2 b f^2 \text {Li}_3\left (-e^{c+d x}\right )}{a^2 d^3}+\frac {2 b f^2 \text {Li}_3\left (e^{c+d x}\right )}{a^2 d^3}-\frac {\left (2 \sqrt {a^2+b^2} f^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (\frac {b x}{-a+\sqrt {a^2+b^2}}\right )}{x} \, dx,x,e^{c+d x}\right )}{a^2 d^3}+\frac {\left (2 \sqrt {a^2+b^2} f^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x}{a+\sqrt {a^2+b^2}}\right )}{x} \, dx,x,e^{c+d x}\right )}{a^2 d^3}\\ &=-\frac {(e+f x)^2}{a d}+\frac {2 b (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a^2 d}-\frac {(e+f x)^2 \coth (c+d x)}{a d}+\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d}-\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d}+\frac {2 f (e+f x) \log \left (1-e^{2 (c+d x)}\right )}{a d^2}+\frac {2 b f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a^2 d^2}-\frac {2 b f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a^2 d^2}+\frac {2 \sqrt {a^2+b^2} f (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^2}-\frac {2 \sqrt {a^2+b^2} f (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d^2}+\frac {f^2 \text {Li}_2\left (e^{2 (c+d x)}\right )}{a d^3}-\frac {2 b f^2 \text {Li}_3\left (-e^{c+d x}\right )}{a^2 d^3}+\frac {2 b f^2 \text {Li}_3\left (e^{c+d x}\right )}{a^2 d^3}-\frac {2 \sqrt {a^2+b^2} f^2 \text {Li}_3\left (-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a^2 d^3}+\frac {2 \sqrt {a^2+b^2} f^2 \text {Li}_3\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a^2 d^3}\\ \end {align*}
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Mathematica [A] time = 7.88, size = 792, normalized size = 1.53 \[ \frac {\sqrt {a^2+b^2} \left (-2 d^2 e^2 \tanh ^{-1}\left (\frac {a+b e^{c+d x}}{\sqrt {a^2+b^2}}\right )+2 d^2 e f x \log \left (\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}+1\right )-2 d^2 e f x \log \left (\frac {b e^{c+d x}}{\sqrt {a^2+b^2}+a}+1\right )+d^2 f^2 x^2 \log \left (\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}+1\right )-d^2 f^2 x^2 \log \left (\frac {b e^{c+d x}}{\sqrt {a^2+b^2}+a}+1\right )+2 d f (e+f x) \text {Li}_2\left (\frac {b e^{c+d x}}{\sqrt {a^2+b^2}-a}\right )-2 d f (e+f x) \text {Li}_2\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )-2 f^2 \text {Li}_3\left (\frac {b e^{c+d x}}{\sqrt {a^2+b^2}-a}\right )+2 f^2 \text {Li}_3\left (-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )\right )}{a^2 d^3}-\frac {2 f \text {Li}_2\left (-e^{-c-d x}\right ) (a f+b d e)+2 f \text {Li}_2\left (e^{-c-d x}\right ) (a f-b d e)+2 d f x \log \left (1-e^{-c-d x}\right ) (b d e-a f)-2 d f x \log \left (e^{-c-d x}+1\right ) (a f+b d e)-d e \left (d x-\log \left (1-e^{c+d x}\right )\right ) (b d e-2 a f)+d e \left (d x-\log \left (e^{c+d x}+1\right )\right ) (2 a f+b d e)+\frac {2 a d^2 (e+f x)^2}{e^{2 c}-1}+b d^2 f^2 x^2 \log \left (1-e^{-c-d x}\right )-b d^2 f^2 x^2 \log \left (e^{-c-d x}+1\right )+2 b f^2 \left (d x \text {Li}_2\left (-e^{-c-d x}\right )+\text {Li}_3\left (-e^{-c-d x}\right )\right )-2 b f^2 \left (d x \text {Li}_2\left (e^{-c-d x}\right )+\text {Li}_3\left (e^{-c-d x}\right )\right )}{a^2 d^3}+\frac {\text {csch}\left (\frac {c}{2}\right ) \text {csch}\left (\frac {c}{2}+\frac {d x}{2}\right ) \left (e^2 \sinh \left (\frac {d x}{2}\right )+2 e f x \sinh \left (\frac {d x}{2}\right )+f^2 x^2 \sinh \left (\frac {d x}{2}\right )\right )}{2 a d}+\frac {\text {sech}\left (\frac {c}{2}\right ) \text {sech}\left (\frac {c}{2}+\frac {d x}{2}\right ) \left (e^2 \left (-\sinh \left (\frac {d x}{2}\right )\right )-2 e f x \sinh \left (\frac {d x}{2}\right )-f^2 x^2 \sinh \left (\frac {d x}{2}\right )\right )}{2 a d} \]
Antiderivative was successfully verified.
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fricas [C] time = 0.58, size = 2729, normalized size = 5.28 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 1.35, size = 0, normalized size = 0.00 \[ \int \frac {\left (f x +e \right )^{2} \left (\coth ^{2}\left (d x +c \right )\right )}{a +b \sinh \left (d x +c \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ e^{2} {\left (\frac {b \log \left (e^{\left (-d x - c\right )} + 1\right )}{a^{2} d} - \frac {b \log \left (e^{\left (-d x - c\right )} - 1\right )}{a^{2} d} + \frac {\sqrt {a^{2} + b^{2}} \log \left (\frac {b e^{\left (-d x - c\right )} - a - \sqrt {a^{2} + b^{2}}}{b e^{\left (-d x - c\right )} - a + \sqrt {a^{2} + b^{2}}}\right )}{a^{2} d} + \frac {2}{{\left (a e^{\left (-2 \, d x - 2 \, c\right )} - a\right )} d}\right )} - \frac {4 \, e f x}{a d} - \frac {2 \, {\left (f^{2} x^{2} + 2 \, e f x\right )}}{a d e^{\left (2 \, d x + 2 \, c\right )} - a d} + \frac {2 \, e f \log \left (e^{\left (d x + c\right )} + 1\right )}{a d^{2}} + \frac {2 \, e f \log \left (e^{\left (d x + c\right )} - 1\right )}{a d^{2}} + \frac {{\left (d^{2} x^{2} \log \left (e^{\left (d x + c\right )} + 1\right ) + 2 \, d x {\rm Li}_2\left (-e^{\left (d x + c\right )}\right ) - 2 \, {\rm Li}_{3}(-e^{\left (d x + c\right )})\right )} b f^{2}}{a^{2} d^{3}} - \frac {{\left (d^{2} x^{2} \log \left (-e^{\left (d x + c\right )} + 1\right ) + 2 \, d x {\rm Li}_2\left (e^{\left (d x + c\right )}\right ) - 2 \, {\rm Li}_{3}(e^{\left (d x + c\right )})\right )} b f^{2}}{a^{2} d^{3}} + \frac {2 \, {\left (b d e f + a f^{2}\right )} {\left (d x \log \left (e^{\left (d x + c\right )} + 1\right ) + {\rm Li}_2\left (-e^{\left (d x + c\right )}\right )\right )}}{a^{2} d^{3}} - \frac {2 \, {\left (b d e f - a f^{2}\right )} {\left (d x \log \left (-e^{\left (d x + c\right )} + 1\right ) + {\rm Li}_2\left (e^{\left (d x + c\right )}\right )\right )}}{a^{2} d^{3}} - \frac {b d^{3} f^{2} x^{3} + 3 \, {\left (b d e f + a f^{2}\right )} d^{2} x^{2}}{3 \, a^{2} d^{3}} + \frac {b d^{3} f^{2} x^{3} + 3 \, {\left (b d e f - a f^{2}\right )} d^{2} x^{2}}{3 \, a^{2} d^{3}} + \int \frac {2 \, {\left ({\left (a^{2} f^{2} e^{c} + b^{2} f^{2} e^{c}\right )} x^{2} + 2 \, {\left (a^{2} e f e^{c} + b^{2} e f e^{c}\right )} x\right )} e^{\left (d x\right )}}{a^{2} b e^{\left (2 \, d x + 2 \, c\right )} + 2 \, a^{3} e^{\left (d x + c\right )} - a^{2} b}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {{\mathrm {coth}\left (c+d\,x\right )}^2\,{\left (e+f\,x\right )}^2}{a+b\,\mathrm {sinh}\left (c+d\,x\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (e + f x\right )^{2} \coth ^{2}{\left (c + d x \right )}}{a + b \sinh {\left (c + d x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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