Optimal. Leaf size=530 \[ \frac {15}{8} c^2 d^2 x \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )^2+\frac {5 c d^2 \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )^3}{8 b \sqrt {c^2 x^2+1}}+\frac {c d^2 \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )^2}{\sqrt {c^2 x^2+1}}-\frac {1}{8} b c d^2 \left (c^2 x^2+1\right )^{3/2} \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )+b c d^2 \sqrt {c^2 x^2+1} \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )+\frac {2 b c d^2 \sqrt {c^2 d x^2+d} \log \left (1-e^{-2 \sinh ^{-1}(c x)}\right ) \left (a+b \sinh ^{-1}(c x)\right )}{\sqrt {c^2 x^2+1}}+\frac {5}{4} c^2 d x \left (c^2 d x^2+d\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (c^2 d x^2+d\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}-\frac {15 b c^3 d^2 x^2 \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )}{8 \sqrt {c^2 x^2+1}}-\frac {b^2 c d^2 \sqrt {c^2 d x^2+d} \text {Li}_2\left (e^{-2 \sinh ^{-1}(c x)}\right )}{\sqrt {c^2 x^2+1}}+\frac {31}{64} b^2 c^2 d^2 x \sqrt {c^2 d x^2+d}+\frac {1}{32} b^2 c^2 d^2 x \left (c^2 x^2+1\right ) \sqrt {c^2 d x^2+d}-\frac {89 b^2 c d^2 \sqrt {c^2 d x^2+d} \sinh ^{-1}(c x)}{64 \sqrt {c^2 x^2+1}} \]
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Rubi [A] time = 0.61, antiderivative size = 530, normalized size of antiderivative = 1.00, number of steps used = 23, number of rules used = 15, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.536, Rules used = {5739, 5684, 5682, 5675, 5661, 321, 215, 5717, 195, 5726, 5659, 3716, 2190, 2279, 2391} \[ \frac {b^2 c d^2 \sqrt {c^2 d x^2+d} \text {PolyLog}\left (2,e^{2 \sinh ^{-1}(c x)}\right )}{\sqrt {c^2 x^2+1}}-\frac {15 b c^3 d^2 x^2 \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )}{8 \sqrt {c^2 x^2+1}}+\frac {15}{8} c^2 d^2 x \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )^2+\frac {5 c d^2 \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )^3}{8 b \sqrt {c^2 x^2+1}}-\frac {c d^2 \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )^2}{\sqrt {c^2 x^2+1}}-\frac {1}{8} b c d^2 \left (c^2 x^2+1\right )^{3/2} \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )+b c d^2 \sqrt {c^2 x^2+1} \sqrt {c^2 d x^2+d} \left (a+b \sinh ^{-1}(c x)\right )+\frac {2 b c d^2 \sqrt {c^2 d x^2+d} \log \left (1-e^{2 \sinh ^{-1}(c x)}\right ) \left (a+b \sinh ^{-1}(c x)\right )}{\sqrt {c^2 x^2+1}}+\frac {5}{4} c^2 d x \left (c^2 d x^2+d\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (c^2 d x^2+d\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\frac {31}{64} b^2 c^2 d^2 x \sqrt {c^2 d x^2+d}+\frac {1}{32} b^2 c^2 d^2 x \left (c^2 x^2+1\right ) \sqrt {c^2 d x^2+d}-\frac {89 b^2 c d^2 \sqrt {c^2 d x^2+d} \sinh ^{-1}(c x)}{64 \sqrt {c^2 x^2+1}} \]
Warning: Unable to verify antiderivative.
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Rule 195
Rule 215
Rule 321
Rule 2190
Rule 2279
Rule 2391
Rule 3716
Rule 5659
Rule 5661
Rule 5675
Rule 5682
Rule 5684
Rule 5717
Rule 5726
Rule 5739
Rubi steps
\begin {align*} \int \frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x^2} \, dx &=-\frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\left (5 c^2 d\right ) \int \left (d+c^2 d x^2\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2 \, dx+\frac {\left (2 b c d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {\left (1+c^2 x^2\right )^2 \left (a+b \sinh ^{-1}(c x)\right )}{x} \, dx}{\sqrt {1+c^2 x^2}}\\ &=\frac {1}{2} b c d^2 \left (1+c^2 x^2\right )^{3/2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )+\frac {5}{4} c^2 d x \left (d+c^2 d x^2\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\frac {1}{4} \left (15 c^2 d^2\right ) \int \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2 \, dx+\frac {\left (2 b c d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {\left (1+c^2 x^2\right ) \left (a+b \sinh ^{-1}(c x)\right )}{x} \, dx}{\sqrt {1+c^2 x^2}}-\frac {\left (b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \left (1+c^2 x^2\right )^{3/2} \, dx}{2 \sqrt {1+c^2 x^2}}-\frac {\left (5 b c^3 d^2 \sqrt {d+c^2 d x^2}\right ) \int x \left (1+c^2 x^2\right ) \left (a+b \sinh ^{-1}(c x)\right ) \, dx}{2 \sqrt {1+c^2 x^2}}\\ &=-\frac {1}{8} b^2 c^2 d^2 x \left (1+c^2 x^2\right ) \sqrt {d+c^2 d x^2}+b c d^2 \sqrt {1+c^2 x^2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1+c^2 x^2\right )^{3/2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )+\frac {15}{8} c^2 d^2 x \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2+\frac {5}{4} c^2 d x \left (d+c^2 d x^2\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\frac {\left (2 b c d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {a+b \sinh ^{-1}(c x)}{x} \, dx}{\sqrt {1+c^2 x^2}}+\frac {\left (15 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {\left (a+b \sinh ^{-1}(c x)\right )^2}{\sqrt {1+c^2 x^2}} \, dx}{8 \sqrt {1+c^2 x^2}}-\frac {\left (3 b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \sqrt {1+c^2 x^2} \, dx}{8 \sqrt {1+c^2 x^2}}+\frac {\left (5 b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \left (1+c^2 x^2\right )^{3/2} \, dx}{8 \sqrt {1+c^2 x^2}}-\frac {\left (b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \sqrt {1+c^2 x^2} \, dx}{\sqrt {1+c^2 x^2}}-\frac {\left (15 b c^3 d^2 \sqrt {d+c^2 d x^2}\right ) \int x \left (a+b \sinh ^{-1}(c x)\right ) \, dx}{4 \sqrt {1+c^2 x^2}}\\ &=-\frac {11}{16} b^2 c^2 d^2 x \sqrt {d+c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1+c^2 x^2\right ) \sqrt {d+c^2 d x^2}-\frac {15 b c^3 d^2 x^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )}{8 \sqrt {1+c^2 x^2}}+b c d^2 \sqrt {1+c^2 x^2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1+c^2 x^2\right )^{3/2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )+\frac {15}{8} c^2 d^2 x \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2+\frac {5}{4} c^2 d x \left (d+c^2 d x^2\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\frac {5 c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^3}{8 b \sqrt {1+c^2 x^2}}+\frac {\left (2 b c d^2 \sqrt {d+c^2 d x^2}\right ) \operatorname {Subst}\left (\int (a+b x) \coth (x) \, dx,x,\sinh ^{-1}(c x)\right )}{\sqrt {1+c^2 x^2}}-\frac {\left (3 b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {1}{\sqrt {1+c^2 x^2}} \, dx}{16 \sqrt {1+c^2 x^2}}+\frac {\left (15 b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \sqrt {1+c^2 x^2} \, dx}{32 \sqrt {1+c^2 x^2}}-\frac {\left (b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {1}{\sqrt {1+c^2 x^2}} \, dx}{2 \sqrt {1+c^2 x^2}}+\frac {\left (15 b^2 c^4 d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {x^2}{\sqrt {1+c^2 x^2}} \, dx}{8 \sqrt {1+c^2 x^2}}\\ &=\frac {31}{64} b^2 c^2 d^2 x \sqrt {d+c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1+c^2 x^2\right ) \sqrt {d+c^2 d x^2}-\frac {11 b^2 c d^2 \sqrt {d+c^2 d x^2} \sinh ^{-1}(c x)}{16 \sqrt {1+c^2 x^2}}-\frac {15 b c^3 d^2 x^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )}{8 \sqrt {1+c^2 x^2}}+b c d^2 \sqrt {1+c^2 x^2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1+c^2 x^2\right )^{3/2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )+\frac {15}{8} c^2 d^2 x \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2}{\sqrt {1+c^2 x^2}}+\frac {5}{4} c^2 d x \left (d+c^2 d x^2\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\frac {5 c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^3}{8 b \sqrt {1+c^2 x^2}}-\frac {\left (4 b c d^2 \sqrt {d+c^2 d x^2}\right ) \operatorname {Subst}\left (\int \frac {e^{2 x} (a+b x)}{1-e^{2 x}} \, dx,x,\sinh ^{-1}(c x)\right )}{\sqrt {1+c^2 x^2}}+\frac {\left (15 b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {1}{\sqrt {1+c^2 x^2}} \, dx}{64 \sqrt {1+c^2 x^2}}-\frac {\left (15 b^2 c^2 d^2 \sqrt {d+c^2 d x^2}\right ) \int \frac {1}{\sqrt {1+c^2 x^2}} \, dx}{16 \sqrt {1+c^2 x^2}}\\ &=\frac {31}{64} b^2 c^2 d^2 x \sqrt {d+c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1+c^2 x^2\right ) \sqrt {d+c^2 d x^2}-\frac {89 b^2 c d^2 \sqrt {d+c^2 d x^2} \sinh ^{-1}(c x)}{64 \sqrt {1+c^2 x^2}}-\frac {15 b c^3 d^2 x^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )}{8 \sqrt {1+c^2 x^2}}+b c d^2 \sqrt {1+c^2 x^2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1+c^2 x^2\right )^{3/2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )+\frac {15}{8} c^2 d^2 x \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2}{\sqrt {1+c^2 x^2}}+\frac {5}{4} c^2 d x \left (d+c^2 d x^2\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\frac {5 c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^3}{8 b \sqrt {1+c^2 x^2}}+\frac {2 b c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right ) \log \left (1-e^{2 \sinh ^{-1}(c x)}\right )}{\sqrt {1+c^2 x^2}}-\frac {\left (2 b^2 c d^2 \sqrt {d+c^2 d x^2}\right ) \operatorname {Subst}\left (\int \log \left (1-e^{2 x}\right ) \, dx,x,\sinh ^{-1}(c x)\right )}{\sqrt {1+c^2 x^2}}\\ &=\frac {31}{64} b^2 c^2 d^2 x \sqrt {d+c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1+c^2 x^2\right ) \sqrt {d+c^2 d x^2}-\frac {89 b^2 c d^2 \sqrt {d+c^2 d x^2} \sinh ^{-1}(c x)}{64 \sqrt {1+c^2 x^2}}-\frac {15 b c^3 d^2 x^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )}{8 \sqrt {1+c^2 x^2}}+b c d^2 \sqrt {1+c^2 x^2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1+c^2 x^2\right )^{3/2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )+\frac {15}{8} c^2 d^2 x \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2}{\sqrt {1+c^2 x^2}}+\frac {5}{4} c^2 d x \left (d+c^2 d x^2\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\frac {5 c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^3}{8 b \sqrt {1+c^2 x^2}}+\frac {2 b c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right ) \log \left (1-e^{2 \sinh ^{-1}(c x)}\right )}{\sqrt {1+c^2 x^2}}-\frac {\left (b^2 c d^2 \sqrt {d+c^2 d x^2}\right ) \operatorname {Subst}\left (\int \frac {\log (1-x)}{x} \, dx,x,e^{2 \sinh ^{-1}(c x)}\right )}{\sqrt {1+c^2 x^2}}\\ &=\frac {31}{64} b^2 c^2 d^2 x \sqrt {d+c^2 d x^2}+\frac {1}{32} b^2 c^2 d^2 x \left (1+c^2 x^2\right ) \sqrt {d+c^2 d x^2}-\frac {89 b^2 c d^2 \sqrt {d+c^2 d x^2} \sinh ^{-1}(c x)}{64 \sqrt {1+c^2 x^2}}-\frac {15 b c^3 d^2 x^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )}{8 \sqrt {1+c^2 x^2}}+b c d^2 \sqrt {1+c^2 x^2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )-\frac {1}{8} b c d^2 \left (1+c^2 x^2\right )^{3/2} \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )+\frac {15}{8} c^2 d^2 x \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^2}{\sqrt {1+c^2 x^2}}+\frac {5}{4} c^2 d x \left (d+c^2 d x^2\right )^{3/2} \left (a+b \sinh ^{-1}(c x)\right )^2-\frac {\left (d+c^2 d x^2\right )^{5/2} \left (a+b \sinh ^{-1}(c x)\right )^2}{x}+\frac {5 c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right )^3}{8 b \sqrt {1+c^2 x^2}}+\frac {2 b c d^2 \sqrt {d+c^2 d x^2} \left (a+b \sinh ^{-1}(c x)\right ) \log \left (1-e^{2 \sinh ^{-1}(c x)}\right )}{\sqrt {1+c^2 x^2}}+\frac {b^2 c d^2 \sqrt {d+c^2 d x^2} \text {Li}_2\left (e^{2 \sinh ^{-1}(c x)}\right )}{\sqrt {1+c^2 x^2}}\\ \end {align*}
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Mathematica [A] time = 2.18, size = 550, normalized size = 1.04 \[ \frac {d^2 \left (288 a^2 c^2 x^2 \sqrt {c^2 x^2+1} \sqrt {c^2 d x^2+d}-256 a^2 \sqrt {c^2 x^2+1} \sqrt {c^2 d x^2+d}+480 a^2 c \sqrt {d} x \sqrt {c^2 x^2+1} \log \left (\sqrt {d} \sqrt {c^2 d x^2+d}+c d x\right )+64 a^2 c^4 x^4 \sqrt {c^2 x^2+1} \sqrt {c^2 d x^2+d}+512 a b c x \sqrt {c^2 d x^2+d} \log (c x)+8 b \sqrt {c^2 d x^2+d} \sinh ^{-1}(c x)^2 \left (60 a c x-32 b \sqrt {c^2 x^2+1}+32 b c x+16 b c x \sinh \left (2 \sinh ^{-1}(c x)\right )+b c x \sinh \left (4 \sinh ^{-1}(c x)\right )\right )-128 a b c x \sqrt {c^2 d x^2+d} \cosh \left (2 \sinh ^{-1}(c x)\right )-4 a b c x \sqrt {c^2 d x^2+d} \cosh \left (4 \sinh ^{-1}(c x)\right )-4 b \sqrt {c^2 d x^2+d} \sinh ^{-1}(c x) \left (128 a \sqrt {c^2 x^2+1}-64 a c x \sinh \left (2 \sinh ^{-1}(c x)\right )-4 a c x \sinh \left (4 \sinh ^{-1}(c x)\right )-128 b c x \log \left (1-e^{-2 \sinh ^{-1}(c x)}\right )+32 b c x \cosh \left (2 \sinh ^{-1}(c x)\right )+b c x \cosh \left (4 \sinh ^{-1}(c x)\right )\right )-256 b^2 c x \sqrt {c^2 d x^2+d} \text {Li}_2\left (e^{-2 \sinh ^{-1}(c x)}\right )+160 b^2 c x \sqrt {c^2 d x^2+d} \sinh ^{-1}(c x)^3+64 b^2 c x \sqrt {c^2 d x^2+d} \sinh \left (2 \sinh ^{-1}(c x)\right )+b^2 c x \sqrt {c^2 d x^2+d} \sinh \left (4 \sinh ^{-1}(c x)\right )\right )}{256 x \sqrt {c^2 x^2+1}} \]
Warning: Unable to verify antiderivative.
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fricas [F] time = 0.76, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (a^{2} c^{4} d^{2} x^{4} + 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left (b^{2} c^{4} d^{2} x^{4} + 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right )} \operatorname {arsinh}\left (c x\right )^{2} + 2 \, {\left (a b c^{4} d^{2} x^{4} + 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right )} \operatorname {arsinh}\left (c x\right )\right )} \sqrt {c^{2} d x^{2} + d}}{x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.45, size = 1223, normalized size = 2.31 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
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 \[ \int \frac {{\left (a+b\,\mathrm {asinh}\left (c\,x\right )\right )}^2\,{\left (d\,c^2\,x^2+d\right )}^{5/2}}{x^2} \,d x \]
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 \[ \int \frac {\left (d \left (c^{2} x^{2} + 1\right )\right )^{\frac {5}{2}} \left (a + b \operatorname {asinh}{\left (c x \right )}\right )^{2}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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