Optimal. Leaf size=381 \[ \frac {b^2 c^2}{12 d^3 \left (1+c^2 x^2\right )}-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (1+c^2 x^2\right )^{3/2}}+\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (1+c^2 x^2\right )}+\frac {6 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 \sinh ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1+c^2 x^2\right )}{6 d^3}+\frac {3 b c^2 \left (a+b \sinh ^{-1}(c x)\right ) \text {PolyLog}\left (2,-e^{2 \sinh ^{-1}(c x)}\right )}{d^3}-\frac {3 b c^2 \left (a+b \sinh ^{-1}(c x)\right ) \text {PolyLog}\left (2,e^{2 \sinh ^{-1}(c x)}\right )}{d^3}-\frac {3 b^2 c^2 \text {PolyLog}\left (3,-e^{2 \sinh ^{-1}(c x)}\right )}{2 d^3}+\frac {3 b^2 c^2 \text {PolyLog}\left (3,e^{2 \sinh ^{-1}(c x)}\right )}{2 d^3} \]
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Rubi [A]
time = 0.55, antiderivative size = 381, normalized size of antiderivative = 1.00, number of steps
used = 23, number of rules used = 19, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.731, Rules used = {5809, 5811,
5799, 5569, 4267, 2611, 2320, 6724, 5787, 266, 5788, 267, 277, 198, 197, 5804, 12, 1265, 907}
\begin {gather*} \frac {3 b c^2 \text {Li}_2\left (-e^{2 \sinh ^{-1}(c x)}\right ) \left (a+b \sinh ^{-1}(c x)\right )}{d^3}-\frac {3 b c^2 \text {Li}_2\left (e^{2 \sinh ^{-1}(c x)}\right ) \left (a+b \sinh ^{-1}(c x)\right )}{d^3}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (c^2 x^2+1\right )}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (c^2 x^2+1\right )^2}-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (c^2 x^2+1\right )^{3/2}}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (c^2 x^2+1\right )^2}+\frac {6 c^2 \tanh ^{-1}\left (e^{2 \sinh ^{-1}(c x)}\right ) \left (a+b \sinh ^{-1}(c x)\right )^2}{d^3}+\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {c^2 x^2+1}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (c^2 x^2+1\right )^{3/2}}-\frac {3 b^2 c^2 \text {Li}_3\left (-e^{2 \sinh ^{-1}(c x)}\right )}{2 d^3}+\frac {3 b^2 c^2 \text {Li}_3\left (e^{2 \sinh ^{-1}(c x)}\right )}{2 d^3}+\frac {b^2 c^2}{12 d^3 \left (c^2 x^2+1\right )}-\frac {7 b^2 c^2 \log \left (c^2 x^2+1\right )}{6 d^3}+\frac {b^2 c^2 \log (x)}{d^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 197
Rule 198
Rule 266
Rule 267
Rule 277
Rule 907
Rule 1265
Rule 2320
Rule 2611
Rule 4267
Rule 5569
Rule 5787
Rule 5788
Rule 5799
Rule 5804
Rule 5809
Rule 5811
Rule 6724
Rubi steps
\begin {align*} \int \frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{x^3 \left (d+c^2 d x^2\right )^3} \, dx &=-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\left (3 c^2\right ) \int \frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{x \left (d+c^2 d x^2\right )^3} \, dx+\frac {(b c) \int \frac {a+b \sinh ^{-1}(c x)}{x^2 \left (1+c^2 x^2\right )^{5/2}} \, dx}{d^3}\\ &=-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \left (1+c^2 x^2\right )^{3/2}}-\frac {8 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {\left (b^2 c^2\right ) \int \frac {-3-12 c^2 x^2-8 c^4 x^4}{3 x \left (1+c^2 x^2\right )^2} \, dx}{d^3}+\frac {\left (3 b c^3\right ) \int \frac {a+b \sinh ^{-1}(c x)}{\left (1+c^2 x^2\right )^{5/2}} \, dx}{2 d^3}-\frac {\left (3 c^2\right ) \int \frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{x \left (d+c^2 d x^2\right )^2} \, dx}{d}\\ &=-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (1+c^2 x^2\right )^{3/2}}-\frac {8 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (1+c^2 x^2\right )}-\frac {\left (b^2 c^2\right ) \int \frac {-3-12 c^2 x^2-8 c^4 x^4}{x \left (1+c^2 x^2\right )^2} \, dx}{3 d^3}+\frac {\left (b c^3\right ) \int \frac {a+b \sinh ^{-1}(c x)}{\left (1+c^2 x^2\right )^{3/2}} \, dx}{d^3}+\frac {\left (3 b c^3\right ) \int \frac {a+b \sinh ^{-1}(c x)}{\left (1+c^2 x^2\right )^{3/2}} \, dx}{d^3}-\frac {\left (b^2 c^4\right ) \int \frac {x}{\left (1+c^2 x^2\right )^2} \, dx}{2 d^3}-\frac {\left (3 c^2\right ) \int \frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{x \left (d+c^2 d x^2\right )} \, dx}{d^2}\\ &=\frac {b^2 c^2}{4 d^3 \left (1+c^2 x^2\right )}-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (1+c^2 x^2\right )^{3/2}}+\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (1+c^2 x^2\right )}-\frac {\left (3 c^2\right ) \text {Subst}\left (\int (a+b x)^2 \text {csch}(x) \text {sech}(x) \, dx,x,\sinh ^{-1}(c x)\right )}{d^3}-\frac {\left (b^2 c^2\right ) \text {Subst}\left (\int \frac {-3-12 c^2 x-8 c^4 x^2}{x \left (1+c^2 x\right )^2} \, dx,x,x^2\right )}{6 d^3}-\frac {\left (b^2 c^4\right ) \int \frac {x}{1+c^2 x^2} \, dx}{d^3}-\frac {\left (3 b^2 c^4\right ) \int \frac {x}{1+c^2 x^2} \, dx}{d^3}\\ &=\frac {b^2 c^2}{4 d^3 \left (1+c^2 x^2\right )}-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (1+c^2 x^2\right )^{3/2}}+\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (1+c^2 x^2\right )}-\frac {2 b^2 c^2 \log \left (1+c^2 x^2\right )}{d^3}-\frac {\left (6 c^2\right ) \text {Subst}\left (\int (a+b x)^2 \text {csch}(2 x) \, dx,x,\sinh ^{-1}(c x)\right )}{d^3}-\frac {\left (b^2 c^2\right ) \text {Subst}\left (\int \left (-\frac {3}{x}-\frac {c^2}{\left (1+c^2 x\right )^2}-\frac {5 c^2}{1+c^2 x}\right ) \, dx,x,x^2\right )}{6 d^3}\\ &=\frac {b^2 c^2}{12 d^3 \left (1+c^2 x^2\right )}-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (1+c^2 x^2\right )^{3/2}}+\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (1+c^2 x^2\right )}+\frac {6 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 \sinh ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1+c^2 x^2\right )}{6 d^3}+\frac {\left (6 b c^2\right ) \text {Subst}\left (\int (a+b x) \log \left (1-e^{2 x}\right ) \, dx,x,\sinh ^{-1}(c x)\right )}{d^3}-\frac {\left (6 b c^2\right ) \text {Subst}\left (\int (a+b x) \log \left (1+e^{2 x}\right ) \, dx,x,\sinh ^{-1}(c x)\right )}{d^3}\\ &=\frac {b^2 c^2}{12 d^3 \left (1+c^2 x^2\right )}-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (1+c^2 x^2\right )^{3/2}}+\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (1+c^2 x^2\right )}+\frac {6 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 \sinh ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1+c^2 x^2\right )}{6 d^3}+\frac {3 b c^2 \left (a+b \sinh ^{-1}(c x)\right ) \text {Li}_2\left (-e^{2 \sinh ^{-1}(c x)}\right )}{d^3}-\frac {3 b c^2 \left (a+b \sinh ^{-1}(c x)\right ) \text {Li}_2\left (e^{2 \sinh ^{-1}(c x)}\right )}{d^3}-\frac {\left (3 b^2 c^2\right ) \text {Subst}\left (\int \text {Li}_2\left (-e^{2 x}\right ) \, dx,x,\sinh ^{-1}(c x)\right )}{d^3}+\frac {\left (3 b^2 c^2\right ) \text {Subst}\left (\int \text {Li}_2\left (e^{2 x}\right ) \, dx,x,\sinh ^{-1}(c x)\right )}{d^3}\\ &=\frac {b^2 c^2}{12 d^3 \left (1+c^2 x^2\right )}-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (1+c^2 x^2\right )^{3/2}}+\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (1+c^2 x^2\right )}+\frac {6 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 \sinh ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1+c^2 x^2\right )}{6 d^3}+\frac {3 b c^2 \left (a+b \sinh ^{-1}(c x)\right ) \text {Li}_2\left (-e^{2 \sinh ^{-1}(c x)}\right )}{d^3}-\frac {3 b c^2 \left (a+b \sinh ^{-1}(c x)\right ) \text {Li}_2\left (e^{2 \sinh ^{-1}(c x)}\right )}{d^3}-\frac {\left (3 b^2 c^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2(-x)}{x} \, dx,x,e^{2 \sinh ^{-1}(c x)}\right )}{2 d^3}+\frac {\left (3 b^2 c^2\right ) \text {Subst}\left (\int \frac {\text {Li}_2(x)}{x} \, dx,x,e^{2 \sinh ^{-1}(c x)}\right )}{2 d^3}\\ &=\frac {b^2 c^2}{12 d^3 \left (1+c^2 x^2\right )}-\frac {b c \left (a+b \sinh ^{-1}(c x)\right )}{d^3 x \left (1+c^2 x^2\right )^{3/2}}-\frac {5 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{6 d^3 \left (1+c^2 x^2\right )^{3/2}}+\frac {4 b c^3 x \left (a+b \sinh ^{-1}(c x)\right )}{3 d^3 \sqrt {1+c^2 x^2}}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{4 d^3 \left (1+c^2 x^2\right )^2}-\frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1+c^2 x^2\right )^2}-\frac {3 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2}{2 d^3 \left (1+c^2 x^2\right )}+\frac {6 c^2 \left (a+b \sinh ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 \sinh ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1+c^2 x^2\right )}{6 d^3}+\frac {3 b c^2 \left (a+b \sinh ^{-1}(c x)\right ) \text {Li}_2\left (-e^{2 \sinh ^{-1}(c x)}\right )}{d^3}-\frac {3 b c^2 \left (a+b \sinh ^{-1}(c x)\right ) \text {Li}_2\left (e^{2 \sinh ^{-1}(c x)}\right )}{d^3}-\frac {3 b^2 c^2 \text {Li}_3\left (-e^{2 \sinh ^{-1}(c x)}\right )}{2 d^3}+\frac {3 b^2 c^2 \text {Li}_3\left (e^{2 \sinh ^{-1}(c x)}\right )}{2 d^3}\\ \end {align*}
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Mathematica [C] Result contains complex when optimal does not.
time = 7.33, size = 688, normalized size = 1.81 \begin {gather*} -\frac {\frac {2 a^2}{x^2}+\frac {a^2 c^2}{\left (1+c^2 x^2\right )^2}+\frac {4 a^2 c^2}{1+c^2 x^2}+12 a^2 c^2 \log (x)-6 a^2 c^2 \log \left (1+c^2 x^2\right )-\frac {1}{6} a b \left (\frac {27 c^2 \left (\sqrt {1+c^2 x^2}-i \sinh ^{-1}(c x)\right )}{i+c x}+\frac {27 c^2 \left (\sqrt {1+c^2 x^2}+i \sinh ^{-1}(c x)\right )}{-i+c x}-\frac {24 \left (c x \sqrt {1+c^2 x^2}+\sinh ^{-1}(c x)\right )}{x^2}+\frac {c^2 \left ((-2 i+c x) \sqrt {1+c^2 x^2}+3 \sinh ^{-1}(c x)\right )}{(-i+c x)^2}+\frac {c^2 \left ((2 i+c x) \sqrt {1+c^2 x^2}+3 \sinh ^{-1}(c x)\right )}{(i+c x)^2}-36 c^2 \left (\sinh ^{-1}(c x) \left (\sinh ^{-1}(c x)-4 \log \left (1+i e^{\sinh ^{-1}(c x)}\right )\right )-4 \text {PolyLog}\left (2,-i e^{\sinh ^{-1}(c x)}\right )\right )-36 c^2 \left (\sinh ^{-1}(c x) \left (\sinh ^{-1}(c x)-4 \log \left (1-i e^{\sinh ^{-1}(c x)}\right )\right )-4 \text {PolyLog}\left (2,i e^{\sinh ^{-1}(c x)}\right )\right )+72 c^2 \left (\sinh ^{-1}(c x) \left (\sinh ^{-1}(c x)-2 \log \left (1-e^{2 \sinh ^{-1}(c x)}\right )\right )-\text {PolyLog}\left (2,e^{2 \sinh ^{-1}(c x)}\right )\right )\right )-4 b^2 c^2 \left (-\frac {i \pi ^3}{8}+\frac {1}{12+12 c^2 x^2}+\frac {c x \sinh ^{-1}(c x)}{6 \left (1+c^2 x^2\right )^{3/2}}+\frac {7 c x \sinh ^{-1}(c x)}{3 \sqrt {1+c^2 x^2}}-\frac {\sqrt {1+c^2 x^2} \sinh ^{-1}(c x)}{c x}-\frac {\sinh ^{-1}(c x)^2}{2 c^2 x^2}-\frac {\sinh ^{-1}(c x)^2}{4 \left (1+c^2 x^2\right )^2}-\frac {\sinh ^{-1}(c x)^2}{1+c^2 x^2}+2 \sinh ^{-1}(c x)^3+3 \sinh ^{-1}(c x)^2 \log \left (1+e^{-2 \sinh ^{-1}(c x)}\right )-3 \sinh ^{-1}(c x)^2 \log \left (1-e^{2 \sinh ^{-1}(c x)}\right )+\log (c x)-\frac {7}{6} \log \left (1+c^2 x^2\right )-3 \sinh ^{-1}(c x) \text {PolyLog}\left (2,-e^{-2 \sinh ^{-1}(c x)}\right )-3 \sinh ^{-1}(c x) \text {PolyLog}\left (2,e^{2 \sinh ^{-1}(c x)}\right )-\frac {3}{2} \text {PolyLog}\left (3,-e^{-2 \sinh ^{-1}(c x)}\right )+\frac {3}{2} \text {PolyLog}\left (3,e^{2 \sinh ^{-1}(c x)}\right )\right )}{4 d^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1364\) vs.
\(2(402)=804\).
time = 6.08, size = 1365, normalized size = 3.58
method | result | size |
derivativedivides | \(\text {Expression too large to display}\) | \(1365\) |
default | \(\text {Expression too large to display}\) | \(1365\) |
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 [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \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*} \frac {\int \frac {a^{2}}{c^{6} x^{9} + 3 c^{4} x^{7} + 3 c^{2} x^{5} + x^{3}}\, dx + \int \frac {b^{2} \operatorname {asinh}^{2}{\left (c x \right )}}{c^{6} x^{9} + 3 c^{4} x^{7} + 3 c^{2} x^{5} + x^{3}}\, dx + \int \frac {2 a b \operatorname {asinh}{\left (c x \right )}}{c^{6} x^{9} + 3 c^{4} x^{7} + 3 c^{2} x^{5} + x^{3}}\, dx}{d^{3}} \end {gather*}
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 \begin {gather*} \text {could not integrate} \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 {{\left (a+b\,\mathrm {asinh}\left (c\,x\right )\right )}^2}{x^3\,{\left (d\,c^2\,x^2+d\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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