Optimal. Leaf size=462 \[ \frac {(e+f x)^3}{3 b f}-\frac {2 (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a d}-\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a b d}+\frac {\sqrt {a^2+b^2} (e+f x)^2 \log \left (1+\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a b d}-\frac {2 f (e+f x) \text {PolyLog}\left (2,-e^{c+d x}\right )}{a d^2}+\frac {2 f (e+f x) \text {PolyLog}\left (2,e^{c+d x}\right )}{a d^2}-\frac {2 \sqrt {a^2+b^2} f (e+f x) \text {PolyLog}\left (2,-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a b d^2}+\frac {2 \sqrt {a^2+b^2} f (e+f x) \text {PolyLog}\left (2,-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a b d^2}+\frac {2 f^2 \text {PolyLog}\left (3,-e^{c+d x}\right )}{a d^3}-\frac {2 f^2 \text {PolyLog}\left (3,e^{c+d x}\right )}{a d^3}+\frac {2 \sqrt {a^2+b^2} f^2 \text {PolyLog}\left (3,-\frac {b e^{c+d x}}{a-\sqrt {a^2+b^2}}\right )}{a b d^3}-\frac {2 \sqrt {a^2+b^2} f^2 \text {PolyLog}\left (3,-\frac {b e^{c+d x}}{a+\sqrt {a^2+b^2}}\right )}{a b d^3} \]
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Rubi [A]
time = 0.77, antiderivative size = 462, normalized size of antiderivative = 1.00, number
of steps used = 27, number of rules used = 13, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.406, Rules
used = {5704, 5558, 3377, 2718, 4267, 2611, 2320, 6724, 5684, 32, 3403, 2296, 2221}
\begin {gather*} \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 b 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 b 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 b 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 b 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 b 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 b d}+\frac {2 f^2 \text {Li}_3\left (-e^{c+d x}\right )}{a d^3}-\frac {2 f^2 \text {Li}_3\left (e^{c+d x}\right )}{a d^3}-\frac {2 f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a d^2}+\frac {2 f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a d^2}-\frac {2 (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a d}+\frac {(e+f x)^3}{3 b f} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rule 2221
Rule 2296
Rule 2320
Rule 2611
Rule 2718
Rule 3377
Rule 3403
Rule 4267
Rule 5558
Rule 5684
Rule 5704
Rule 6724
Rubi steps
\begin {align*} \int \frac {(e+f x)^2 \cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx &=\frac {\int (e+f x)^2 \cosh (c+d x) \coth (c+d x) \, dx}{a}-\frac {b \int \frac {(e+f x)^2 \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx}{a}\\ &=\frac {\int (e+f x)^2 \text {csch}(c+d x) \, dx}{a}+\frac {\int (e+f x)^2 \, dx}{b}-\frac {\left (a^2+b^2\right ) \int \frac {(e+f x)^2}{a+b \sinh (c+d x)} \, dx}{a b}\\ &=\frac {(e+f x)^3}{3 b f}-\frac {2 (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a d}-\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 b}-\frac {(2 f) \int (e+f x) \log \left (1-e^{c+d x}\right ) \, dx}{a d}+\frac {(2 f) \int (e+f x) \log \left (1+e^{c+d x}\right ) \, dx}{a d}\\ &=\frac {(e+f x)^3}{3 b f}-\frac {2 (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{a d}-\frac {2 f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a d^2}+\frac {2 f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a d^2}-\frac {\left (2 \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}+\frac {\left (2 \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}+\frac {\left (2 f^2\right ) \int \text {Li}_2\left (-e^{c+d x}\right ) \, dx}{a d^2}-\frac {\left (2 f^2\right ) \int \text {Li}_2\left (e^{c+d x}\right ) \, dx}{a d^2}\\ &=\frac {(e+f x)^3}{3 b f}-\frac {2 (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{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 b 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 b d}-\frac {2 f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a d^2}+\frac {2 f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a d^2}+\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 b 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 b d}+\frac {\left (2 f^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2(-x)}{x} \, dx,x,e^{c+d x}\right )}{a d^3}-\frac {\left (2 f^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2(x)}{x} \, dx,x,e^{c+d x}\right )}{a d^3}\\ &=\frac {(e+f x)^3}{3 b f}-\frac {2 (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{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 b 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 b d}-\frac {2 f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a d^2}+\frac {2 f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a 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 b 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 b d^2}+\frac {2 f^2 \text {Li}_3\left (-e^{c+d x}\right )}{a d^3}-\frac {2 f^2 \text {Li}_3\left (e^{c+d x}\right )}{a 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 b 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 b d^2}\\ &=\frac {(e+f x)^3}{3 b f}-\frac {2 (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{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 b 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 b d}-\frac {2 f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a d^2}+\frac {2 f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a 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 b 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 b d^2}+\frac {2 f^2 \text {Li}_3\left (-e^{c+d x}\right )}{a d^3}-\frac {2 f^2 \text {Li}_3\left (e^{c+d x}\right )}{a d^3}+\frac {\left (2 \sqrt {a^2+b^2} f^2\right ) \text {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 b d^3}-\frac {\left (2 \sqrt {a^2+b^2} f^2\right ) \text {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 b d^3}\\ &=\frac {(e+f x)^3}{3 b f}-\frac {2 (e+f x)^2 \tanh ^{-1}\left (e^{c+d x}\right )}{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 b 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 b d}-\frac {2 f (e+f x) \text {Li}_2\left (-e^{c+d x}\right )}{a d^2}+\frac {2 f (e+f x) \text {Li}_2\left (e^{c+d x}\right )}{a 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 b 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 b d^2}+\frac {2 f^2 \text {Li}_3\left (-e^{c+d x}\right )}{a d^3}-\frac {2 f^2 \text {Li}_3\left (e^{c+d x}\right )}{a 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 b 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 b d^3}\\ \end {align*}
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Mathematica [A]
time = 3.16, size = 815, normalized size = 1.76 \begin {gather*} \frac {x \left (3 e^2+3 e f x+f^2 x^2\right )}{3 b}+\frac {-2 d^2 e^2 \tanh ^{-1}\left (e^{c+d x}\right )+2 d^2 e f x \log \left (1-e^{c+d x}\right )+d^2 f^2 x^2 \log \left (1-e^{c+d x}\right )-2 d^2 e f x \log \left (1+e^{c+d x}\right )-d^2 f^2 x^2 \log \left (1+e^{c+d x}\right )-2 d f (e+f x) \text {PolyLog}\left (2,-e^{c+d x}\right )+2 d f (e+f x) \text {PolyLog}\left (2,e^{c+d x}\right )+2 f^2 \text {PolyLog}\left (3,-e^{c+d x}\right )-2 f^2 \text {PolyLog}\left (3,e^{c+d x}\right )}{a d^3}-\frac {\left (a^2+b^2\right ) \left (\frac {2 d^2 e^2 \text {ArcTan}\left (\frac {a+b e^{c+d x}}{\sqrt {-a^2-b^2}}\right )}{\sqrt {-a^2-b^2}}+\frac {2 d^2 e e^c f x \log \left (1+\frac {b e^{2 c+d x}}{a e^c-\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{\sqrt {\left (a^2+b^2\right ) e^{2 c}}}+\frac {d^2 e^c f^2 x^2 \log \left (1+\frac {b e^{2 c+d x}}{a e^c-\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{\sqrt {\left (a^2+b^2\right ) e^{2 c}}}-\frac {2 d^2 e e^c f x \log \left (1+\frac {b e^{2 c+d x}}{a e^c+\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{\sqrt {\left (a^2+b^2\right ) e^{2 c}}}-\frac {d^2 e^c f^2 x^2 \log \left (1+\frac {b e^{2 c+d x}}{a e^c+\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{\sqrt {\left (a^2+b^2\right ) e^{2 c}}}+\frac {2 d e^c f (e+f x) \text {PolyLog}\left (2,-\frac {b e^{2 c+d x}}{a e^c-\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{\sqrt {\left (a^2+b^2\right ) e^{2 c}}}-\frac {2 d e^c f (e+f x) \text {PolyLog}\left (2,-\frac {b e^{2 c+d x}}{a e^c+\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{\sqrt {\left (a^2+b^2\right ) e^{2 c}}}-\frac {2 e^c f^2 \text {PolyLog}\left (3,-\frac {b e^{2 c+d x}}{a e^c-\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{\sqrt {\left (a^2+b^2\right ) e^{2 c}}}+\frac {2 e^c f^2 \text {PolyLog}\left (3,-\frac {b e^{2 c+d x}}{a e^c+\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{\sqrt {\left (a^2+b^2\right ) e^{2 c}}}\right )}{a b d^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 3.16, size = 0, normalized size = 0.00 \[\int \frac {\left (f x +e \right )^{2} \cosh \left (d x +c \right ) \coth \left (d x +c \right )}{a +b \sinh \left (d x +c \right )}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1227 vs.
\(2 (429) = 858\).
time = 0.43, size = 1227, normalized size = 2.66 \begin {gather*} \frac {a d^{3} f^{2} x^{3} + 3 \, a d^{3} f x^{2} \cosh \left (1\right ) + 3 \, a d^{3} x \cosh \left (1\right )^{2} + 3 \, a d^{3} x \sinh \left (1\right )^{2} + 6 \, b f^{2} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left (3, \frac {a \cosh \left (d x + c\right ) + a \sinh \left (d x + c\right ) + {\left (b \cosh \left (d x + c\right ) + b \sinh \left (d x + c\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}}}{b}\right ) - 6 \, b f^{2} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left (3, \frac {a \cosh \left (d x + c\right ) + a \sinh \left (d x + c\right ) - {\left (b \cosh \left (d x + c\right ) + b \sinh \left (d x + c\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}}}{b}\right ) - 6 \, b f^{2} {\rm polylog}\left (3, \cosh \left (d x + c\right ) + \sinh \left (d x + c\right )\right ) + 6 \, b f^{2} {\rm polylog}\left (3, -\cosh \left (d x + c\right ) - \sinh \left (d x + c\right )\right ) - 6 \, {\left (b d f^{2} x + b d f \cosh \left (1\right ) + b d f \sinh \left (1\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left (\frac {a \cosh \left (d x + c\right ) + a \sinh \left (d x + c\right ) + {\left (b \cosh \left (d x + c\right ) + b \sinh \left (d x + c\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right ) + 6 \, {\left (b d f^{2} x + b d f \cosh \left (1\right ) + b d f \sinh \left (1\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left (\frac {a \cosh \left (d x + c\right ) + a \sinh \left (d x + c\right ) - {\left (b \cosh \left (d x + c\right ) + b \sinh \left (d x + c\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right ) + 3 \, {\left (b c^{2} f^{2} - 2 \, b c d f \cosh \left (1\right ) + b d^{2} \cosh \left (1\right )^{2} + b d^{2} \sinh \left (1\right )^{2} - 2 \, {\left (b c d f - b d^{2} \cosh \left (1\right )\right )} \sinh \left (1\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} \log \left (2 \, b \cosh \left (d x + c\right ) + 2 \, b \sinh \left (d x + c\right ) + 2 \, b \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} + 2 \, a\right ) - 3 \, {\left (b c^{2} f^{2} - 2 \, b c d f \cosh \left (1\right ) + b d^{2} \cosh \left (1\right )^{2} + b d^{2} \sinh \left (1\right )^{2} - 2 \, {\left (b c d f - b d^{2} \cosh \left (1\right )\right )} \sinh \left (1\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} \log \left (2 \, b \cosh \left (d x + c\right ) + 2 \, b \sinh \left (d x + c\right ) - 2 \, b \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} + 2 \, a\right ) - 3 \, {\left (b d^{2} f^{2} x^{2} - b c^{2} f^{2} + 2 \, {\left (b d^{2} f x + b c d f\right )} \cosh \left (1\right ) + 2 \, {\left (b d^{2} f x + b c d f\right )} \sinh \left (1\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} \log \left (-\frac {a \cosh \left (d x + c\right ) + a \sinh \left (d x + c\right ) + {\left (b \cosh \left (d x + c\right ) + b \sinh \left (d x + c\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} - b}{b}\right ) + 3 \, {\left (b d^{2} f^{2} x^{2} - b c^{2} f^{2} + 2 \, {\left (b d^{2} f x + b c d f\right )} \cosh \left (1\right ) + 2 \, {\left (b d^{2} f x + b c d f\right )} \sinh \left (1\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} \log \left (-\frac {a \cosh \left (d x + c\right ) + a \sinh \left (d x + c\right ) - {\left (b \cosh \left (d x + c\right ) + b \sinh \left (d x + c\right )\right )} \sqrt {\frac {a^{2} + b^{2}}{b^{2}}} - b}{b}\right ) + 6 \, {\left (b d f^{2} x + b d f \cosh \left (1\right ) + b d f \sinh \left (1\right )\right )} {\rm Li}_2\left (\cosh \left (d x + c\right ) + \sinh \left (d x + c\right )\right ) - 6 \, {\left (b d f^{2} x + b d f \cosh \left (1\right ) + b d f \sinh \left (1\right )\right )} {\rm Li}_2\left (-\cosh \left (d x + c\right ) - \sinh \left (d x + c\right )\right ) - 3 \, {\left (b d^{2} f^{2} x^{2} + 2 \, b d^{2} f x \cosh \left (1\right ) + b d^{2} \cosh \left (1\right )^{2} + b d^{2} \sinh \left (1\right )^{2} + 2 \, {\left (b d^{2} f x + b d^{2} \cosh \left (1\right )\right )} \sinh \left (1\right )\right )} \log \left (\cosh \left (d x + c\right ) + \sinh \left (d x + c\right ) + 1\right ) + 3 \, {\left (b c^{2} f^{2} - 2 \, b c d f \cosh \left (1\right ) + b d^{2} \cosh \left (1\right )^{2} + b d^{2} \sinh \left (1\right )^{2} - 2 \, {\left (b c d f - b d^{2} \cosh \left (1\right )\right )} \sinh \left (1\right )\right )} \log \left (\cosh \left (d x + c\right ) + \sinh \left (d x + c\right ) - 1\right ) + 3 \, {\left (b d^{2} f^{2} x^{2} - b c^{2} f^{2} + 2 \, {\left (b d^{2} f x + b c d f\right )} \cosh \left (1\right ) + 2 \, {\left (b d^{2} f x + b c d f\right )} \sinh \left (1\right )\right )} \log \left (-\cosh \left (d x + c\right ) - \sinh \left (d x + c\right ) + 1\right ) + 3 \, {\left (a d^{3} f x^{2} + 2 \, a d^{3} x \cosh \left (1\right )\right )} \sinh \left (1\right )}{3 \, a b d^{3}} \end {gather*}
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 \begin {gather*} \int \frac {\left (e + f x\right )^{2} \cosh {\left (c + d x \right )} \coth {\left (c + d x \right )}}{a + b \sinh {\left (c + d x \right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \int \frac {\mathrm {cosh}\left (c+d\,x\right )\,\mathrm {coth}\left (c+d\,x\right )\,{\left (e+f\,x\right )}^2}{a+b\,\mathrm {sinh}\left (c+d\,x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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