Optimal. Leaf size=550 \[ \frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {c^2 (-d)-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {c^2 (-d)-e}}+1\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{\sqrt {c^2 (-d)-e}+c \sqrt {-d}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{\sqrt {c^2 (-d)-e}+c \sqrt {-d}}+1\right )}{2 d^2}-\frac {e \left (a+b \cosh ^{-1}(c x)\right )^2}{b d^2}-\frac {e \log \left (e^{-2 \cosh ^{-1}(c x)}+1\right ) \left (a+b \cosh ^{-1}(c x)\right )}{d^2}-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac {b e \text {Li}_2\left (-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-d c^2-e}}\right )}{2 d^2}+\frac {b e \text {Li}_2\left (\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-d c^2-e}}\right )}{2 d^2}+\frac {b e \text {Li}_2\left (-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{\sqrt {-d} c+\sqrt {-d c^2-e}}\right )}{2 d^2}+\frac {b e \text {Li}_2\left (\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{\sqrt {-d} c+\sqrt {-d c^2-e}}\right )}{2 d^2}+\frac {b e \text {Li}_2\left (-e^{-2 \cosh ^{-1}(c x)}\right )}{2 d^2}+\frac {b c \sqrt {c x-1} \sqrt {c x+1}}{2 d x} \]
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Rubi [A] time = 0.95, antiderivative size = 531, normalized size of antiderivative = 0.97, number of steps used = 27, number of rules used = 10, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.476, Rules used = {5792, 5662, 95, 5660, 3718, 2190, 2279, 2391, 5800, 5562} \[ \frac {b e \text {PolyLog}\left (2,-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {c^2 (-d)-e}}\right )}{2 d^2}+\frac {b e \text {PolyLog}\left (2,\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {c^2 (-d)-e}}\right )}{2 d^2}+\frac {b e \text {PolyLog}\left (2,-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{\sqrt {c^2 (-d)-e}+c \sqrt {-d}}\right )}{2 d^2}+\frac {b e \text {PolyLog}\left (2,\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{\sqrt {c^2 (-d)-e}+c \sqrt {-d}}\right )}{2 d^2}-\frac {b e \text {PolyLog}\left (2,-e^{2 \cosh ^{-1}(c x)}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {c^2 (-d)-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {c^2 (-d)-e}}+1\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{\sqrt {c^2 (-d)-e}+c \sqrt {-d}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{\sqrt {c^2 (-d)-e}+c \sqrt {-d}}+1\right )}{2 d^2}-\frac {e \log \left (e^{2 \cosh ^{-1}(c x)}+1\right ) \left (a+b \cosh ^{-1}(c x)\right )}{d^2}-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac {b c \sqrt {c x-1} \sqrt {c x+1}}{2 d x} \]
Warning: Unable to verify antiderivative.
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Rule 95
Rule 2190
Rule 2279
Rule 2391
Rule 3718
Rule 5562
Rule 5660
Rule 5662
Rule 5792
Rule 5800
Rubi steps
\begin {align*} \int \frac {a+b \cosh ^{-1}(c x)}{x^3 \left (d+e x^2\right )} \, dx &=\int \left (\frac {a+b \cosh ^{-1}(c x)}{d x^3}-\frac {e \left (a+b \cosh ^{-1}(c x)\right )}{d^2 x}+\frac {e^2 x \left (a+b \cosh ^{-1}(c x)\right )}{d^2 \left (d+e x^2\right )}\right ) \, dx\\ &=\frac {\int \frac {a+b \cosh ^{-1}(c x)}{x^3} \, dx}{d}-\frac {e \int \frac {a+b \cosh ^{-1}(c x)}{x} \, dx}{d^2}+\frac {e^2 \int \frac {x \left (a+b \cosh ^{-1}(c x)\right )}{d+e x^2} \, dx}{d^2}\\ &=-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac {(b c) \int \frac {1}{x^2 \sqrt {-1+c x} \sqrt {1+c x}} \, dx}{2 d}-\frac {e \operatorname {Subst}\left (\int (a+b x) \tanh (x) \, dx,x,\cosh ^{-1}(c x)\right )}{d^2}+\frac {e^2 \int \left (-\frac {a+b \cosh ^{-1}(c x)}{2 \sqrt {e} \left (\sqrt {-d}-\sqrt {e} x\right )}+\frac {a+b \cosh ^{-1}(c x)}{2 \sqrt {e} \left (\sqrt {-d}+\sqrt {e} x\right )}\right ) \, dx}{d^2}\\ &=\frac {b c \sqrt {-1+c x} \sqrt {1+c x}}{2 d x}-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right )^2}{2 b d^2}-\frac {(2 e) \operatorname {Subst}\left (\int \frac {e^{2 x} (a+b x)}{1+e^{2 x}} \, dx,x,\cosh ^{-1}(c x)\right )}{d^2}-\frac {e^{3/2} \int \frac {a+b \cosh ^{-1}(c x)}{\sqrt {-d}-\sqrt {e} x} \, dx}{2 d^2}+\frac {e^{3/2} \int \frac {a+b \cosh ^{-1}(c x)}{\sqrt {-d}+\sqrt {e} x} \, dx}{2 d^2}\\ &=\frac {b c \sqrt {-1+c x} \sqrt {1+c x}}{2 d x}-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right )^2}{2 b d^2}-\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+e^{2 \cosh ^{-1}(c x)}\right )}{d^2}+\frac {(b e) \operatorname {Subst}\left (\int \log \left (1+e^{2 x}\right ) \, dx,x,\cosh ^{-1}(c x)\right )}{d^2}-\frac {e^{3/2} \operatorname {Subst}\left (\int \frac {(a+b x) \sinh (x)}{c \sqrt {-d}-\sqrt {e} \cosh (x)} \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}+\frac {e^{3/2} \operatorname {Subst}\left (\int \frac {(a+b x) \sinh (x)}{c \sqrt {-d}+\sqrt {e} \cosh (x)} \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}\\ &=\frac {b c \sqrt {-1+c x} \sqrt {1+c x}}{2 d x}-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}-\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+e^{2 \cosh ^{-1}(c x)}\right )}{d^2}+\frac {(b e) \operatorname {Subst}\left (\int \frac {\log (1+x)}{x} \, dx,x,e^{2 \cosh ^{-1}(c x)}\right )}{2 d^2}-\frac {e^{3/2} \operatorname {Subst}\left (\int \frac {e^x (a+b x)}{c \sqrt {-d}-\sqrt {-c^2 d-e}-\sqrt {e} e^x} \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}-\frac {e^{3/2} \operatorname {Subst}\left (\int \frac {e^x (a+b x)}{c \sqrt {-d}+\sqrt {-c^2 d-e}-\sqrt {e} e^x} \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}+\frac {e^{3/2} \operatorname {Subst}\left (\int \frac {e^x (a+b x)}{c \sqrt {-d}-\sqrt {-c^2 d-e}+\sqrt {e} e^x} \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}+\frac {e^{3/2} \operatorname {Subst}\left (\int \frac {e^x (a+b x)}{c \sqrt {-d}+\sqrt {-c^2 d-e}+\sqrt {e} e^x} \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}\\ &=\frac {b c \sqrt {-1+c x} \sqrt {1+c x}}{2 d x}-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{2 d^2}-\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+e^{2 \cosh ^{-1}(c x)}\right )}{d^2}-\frac {b e \text {Li}_2\left (-e^{2 \cosh ^{-1}(c x)}\right )}{2 d^2}-\frac {(b e) \operatorname {Subst}\left (\int \log \left (1-\frac {\sqrt {e} e^x}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right ) \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}-\frac {(b e) \operatorname {Subst}\left (\int \log \left (1+\frac {\sqrt {e} e^x}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right ) \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}-\frac {(b e) \operatorname {Subst}\left (\int \log \left (1-\frac {\sqrt {e} e^x}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right ) \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}-\frac {(b e) \operatorname {Subst}\left (\int \log \left (1+\frac {\sqrt {e} e^x}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right ) \, dx,x,\cosh ^{-1}(c x)\right )}{2 d^2}\\ &=\frac {b c \sqrt {-1+c x} \sqrt {1+c x}}{2 d x}-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{2 d^2}-\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+e^{2 \cosh ^{-1}(c x)}\right )}{d^2}-\frac {b e \text {Li}_2\left (-e^{2 \cosh ^{-1}(c x)}\right )}{2 d^2}-\frac {(b e) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {\sqrt {e} x}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{x} \, dx,x,e^{\cosh ^{-1}(c x)}\right )}{2 d^2}-\frac {(b e) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {\sqrt {e} x}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{x} \, dx,x,e^{\cosh ^{-1}(c x)}\right )}{2 d^2}-\frac {(b e) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {\sqrt {e} x}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{x} \, dx,x,e^{\cosh ^{-1}(c x)}\right )}{2 d^2}-\frac {(b e) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {\sqrt {e} x}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{x} \, dx,x,e^{\cosh ^{-1}(c x)}\right )}{2 d^2}\\ &=\frac {b c \sqrt {-1+c x} \sqrt {1+c x}}{2 d x}-\frac {a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{2 d^2}-\frac {e \left (a+b \cosh ^{-1}(c x)\right ) \log \left (1+e^{2 \cosh ^{-1}(c x)}\right )}{d^2}+\frac {b e \text {Li}_2\left (-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {b e \text {Li}_2\left (\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}-\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {b e \text {Li}_2\left (-\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{2 d^2}+\frac {b e \text {Li}_2\left (\frac {\sqrt {e} e^{\cosh ^{-1}(c x)}}{c \sqrt {-d}+\sqrt {-c^2 d-e}}\right )}{2 d^2}-\frac {b e \text {Li}_2\left (-e^{2 \cosh ^{-1}(c x)}\right )}{2 d^2}\\ \end {align*}
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Mathematica [C] time = 1.44, size = 479, normalized size = 0.87 \[ \frac {2 a e \log \left (d+e x^2\right )-\frac {2 a d}{x^2}-4 a e \log (x)+b \left (-e \text {Li}_2\left (-\frac {\left (2 d c^2+e-2 \sqrt {c^2 d \left (d c^2+e\right )}\right ) e^{-2 \cosh ^{-1}(c x)}}{e}\right )-e \text {Li}_2\left (-\frac {\left (2 d c^2+e+2 \sqrt {c^2 d \left (d c^2+e\right )}\right ) e^{-2 \cosh ^{-1}(c x)}}{e}\right )+4 i e \sin ^{-1}\left (\sqrt {\frac {c^2 d}{e}+1}\right ) \tanh ^{-1}\left (\frac {c d \sqrt {\frac {c x-1}{c x+1}} (c x+1)}{x \sqrt {c^2 d \left (c^2 d+e\right )}}\right )+2 e \cosh ^{-1}(c x) \log \left (\frac {\left (-2 \sqrt {c^2 d \left (c^2 d+e\right )}+2 c^2 d+e\right ) e^{-2 \cosh ^{-1}(c x)}}{e}+1\right )+2 e \cosh ^{-1}(c x) \log \left (\frac {\left (2 \sqrt {c^2 d \left (c^2 d+e\right )}+2 c^2 d+e\right ) e^{-2 \cosh ^{-1}(c x)}}{e}+1\right )-2 i e \sin ^{-1}\left (\sqrt {\frac {c^2 d}{e}+1}\right ) \log \left (\frac {\left (-2 \sqrt {c^2 d \left (c^2 d+e\right )}+2 c^2 d+e\right ) e^{-2 \cosh ^{-1}(c x)}}{e}+1\right )+2 i e \sin ^{-1}\left (\sqrt {\frac {c^2 d}{e}+1}\right ) \log \left (\frac {\left (2 \sqrt {c^2 d \left (c^2 d+e\right )}+2 c^2 d+e\right ) e^{-2 \cosh ^{-1}(c x)}}{e}+1\right )-\frac {2 d \cosh ^{-1}(c x)}{x^2}+\frac {2 c d \sqrt {\frac {c x-1}{c x+1}} (c x+1)}{x}+2 e \text {Li}_2\left (-e^{-2 \cosh ^{-1}(c x)}\right )-4 e \cosh ^{-1}(c x) \log \left (e^{-2 \cosh ^{-1}(c x)}+1\right )\right )}{4 d^2} \]
Warning: Unable to verify antiderivative.
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fricas [F] time = 0.52, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b \operatorname {arcosh}\left (c x\right ) + a}{e x^{5} + d x^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {b \operatorname {arcosh}\left (c x\right ) + a}{{\left (e x^{2} + d\right )} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.42, size = 462, normalized size = 0.84 \[ -\frac {a}{2 d \,x^{2}}-\frac {a e \ln \left (c x \right )}{d^{2}}+\frac {a e \ln \left (c^{2} x^{2} e +c^{2} d \right )}{2 d^{2}}+\frac {b c \sqrt {c x -1}\, \sqrt {c x +1}}{2 d x}-\frac {c^{2} b}{2 d}-\frac {b \,\mathrm {arccosh}\left (c x \right )}{2 d \,x^{2}}+\frac {b \,e^{2} \left (\munderset {\textit {\_R1} =\RootOf \left (e \,\textit {\_Z}^{4}+\left (4 c^{2} d +2 e \right ) \textit {\_Z}^{2}+e \right )}{\sum }\frac {\left (\textit {\_R1}^{2}+1\right ) \left (\mathrm {arccosh}\left (c x \right ) \ln \left (\frac {\textit {\_R1} -c x -\sqrt {c x -1}\, \sqrt {c x +1}}{\textit {\_R1}}\right )+\dilog \left (\frac {\textit {\_R1} -c x -\sqrt {c x -1}\, \sqrt {c x +1}}{\textit {\_R1}}\right )\right )}{\textit {\_R1}^{2} e +2 c^{2} d +e}\right )}{4 d^{2}}-\frac {b e \,\mathrm {arccosh}\left (c x \right ) \ln \left (1+i \left (c x +\sqrt {c x -1}\, \sqrt {c x +1}\right )\right )}{d^{2}}-\frac {b e \,\mathrm {arccosh}\left (c x \right ) \ln \left (1-i \left (c x +\sqrt {c x -1}\, \sqrt {c x +1}\right )\right )}{d^{2}}-\frac {b e \dilog \left (1+i \left (c x +\sqrt {c x -1}\, \sqrt {c x +1}\right )\right )}{d^{2}}-\frac {b e \dilog \left (1-i \left (c x +\sqrt {c x -1}\, \sqrt {c x +1}\right )\right )}{d^{2}}+\frac {b e \left (\munderset {\textit {\_R1} =\RootOf \left (e \,\textit {\_Z}^{4}+\left (4 c^{2} d +2 e \right ) \textit {\_Z}^{2}+e \right )}{\sum }\frac {\left (\textit {\_R1}^{2} e +4 c^{2} d +e \right ) \left (\mathrm {arccosh}\left (c x \right ) \ln \left (\frac {\textit {\_R1} -c x -\sqrt {c x -1}\, \sqrt {c x +1}}{\textit {\_R1}}\right )+\dilog \left (\frac {\textit {\_R1} -c x -\sqrt {c x -1}\, \sqrt {c x +1}}{\textit {\_R1}}\right )\right )}{\textit {\_R1}^{2} e +2 c^{2} d +e}\right )}{4 d^{2}} \]
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 \[ \frac {1}{2} \, a {\left (\frac {e \log \left (e x^{2} + d\right )}{d^{2}} - \frac {2 \, e \log \relax (x)}{d^{2}} - \frac {1}{d x^{2}}\right )} + b \int \frac {\log \left (c x + \sqrt {c x + 1} \sqrt {c x - 1}\right )}{e x^{5} + d x^{3}}\,{d x} \]
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 \[ \int \frac {a+b\,\mathrm {acosh}\left (c\,x\right )}{x^3\,\left (e\,x^2+d\right )} \,d x \]
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 \[ \int \frac {a + b \operatorname {acosh}{\left (c x \right )}}{x^{3} \left (d + e x^{2}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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