Optimal. Leaf size=679 \[ -\frac{c^2 (a x+1)^{11/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (a x+1)^{7/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (a x+1)^{3/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (a x+1)^{3/4} (1-a x)^{9/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (a x+1)^{3/4} (1-a x)^{5/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (a x+1)^{3/4} \sqrt [4]{1-a x} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left (\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{a x+1}}+1\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left (\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{a x+1}}+1\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \tan ^{-1}\left (1-\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{a x+1}}\right )}{512 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \tan ^{-1}\left (\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{a x+1}}+1\right )}{512 \sqrt{2} a \sqrt{1-a^2 x^2}} \]
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Rubi [A] time = 0.392367, antiderivative size = 679, normalized size of antiderivative = 1., number of steps used = 19, number of rules used = 11, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.423, Rules used = {6143, 6140, 50, 63, 240, 211, 1165, 628, 1162, 617, 204} \[ -\frac{c^2 (a x+1)^{11/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (a x+1)^{7/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (a x+1)^{3/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (a x+1)^{3/4} (1-a x)^{9/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (a x+1)^{3/4} (1-a x)^{5/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (a x+1)^{3/4} \sqrt [4]{1-a x} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left (\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{a x+1}}+1\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left (\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{a x+1}}+1\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \tan ^{-1}\left (1-\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{a x+1}}\right )}{512 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \tan ^{-1}\left (\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{a x+1}}+1\right )}{512 \sqrt{2} a \sqrt{1-a^2 x^2}} \]
Antiderivative was successfully verified.
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Rule 6143
Rule 6140
Rule 50
Rule 63
Rule 240
Rule 211
Rule 1165
Rule 628
Rule 1162
Rule 617
Rule 204
Rubi steps
\begin{align*} \int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left (c-a^2 c x^2\right )^{5/2} \, dx &=\frac{\left (c^2 \sqrt{c-a^2 c x^2}\right ) \int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left (1-a^2 x^2\right )^{5/2} \, dx}{\sqrt{1-a^2 x^2}}\\ &=\frac{\left (c^2 \sqrt{c-a^2 c x^2}\right ) \int (1-a x)^{9/4} (1+a x)^{11/4} \, dx}{\sqrt{1-a^2 x^2}}\\ &=-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{\left (11 c^2 \sqrt{c-a^2 c x^2}\right ) \int (1-a x)^{9/4} (1+a x)^{7/4} \, dx}{12 \sqrt{1-a^2 x^2}}\\ &=-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{\left (77 c^2 \sqrt{c-a^2 c x^2}\right ) \int (1-a x)^{9/4} (1+a x)^{3/4} \, dx}{120 \sqrt{1-a^2 x^2}}\\ &=-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{\left (77 c^2 \sqrt{c-a^2 c x^2}\right ) \int \frac{(1-a x)^{9/4}}{\sqrt [4]{1+a x}} \, dx}{320 \sqrt{1-a^2 x^2}}\\ &=\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \int \frac{(1-a x)^{5/4}}{\sqrt [4]{1+a x}} \, dx}{640 \sqrt{1-a^2 x^2}}\\ &=\frac{231 c^2 (1-a x)^{5/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \int \frac{\sqrt [4]{1-a x}}{\sqrt [4]{1+a x}} \, dx}{512 \sqrt{1-a^2 x^2}}\\ &=\frac{231 c^2 \sqrt [4]{1-a x} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (1-a x)^{5/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \int \frac{1}{(1-a x)^{3/4} \sqrt [4]{1+a x}} \, dx}{1024 \sqrt{1-a^2 x^2}}\\ &=\frac{231 c^2 \sqrt [4]{1-a x} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (1-a x)^{5/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{1}{\sqrt [4]{2-x^4}} \, dx,x,\sqrt [4]{1-a x}\right )}{256 a \sqrt{1-a^2 x^2}}\\ &=\frac{231 c^2 \sqrt [4]{1-a x} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (1-a x)^{5/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{1}{1+x^4} \, dx,x,\frac{\sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{256 a \sqrt{1-a^2 x^2}}\\ &=\frac{231 c^2 \sqrt [4]{1-a x} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (1-a x)^{5/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{1-x^2}{1+x^4} \, dx,x,\frac{\sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{512 a \sqrt{1-a^2 x^2}}-\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{1+x^2}{1+x^4} \, dx,x,\frac{\sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{512 a \sqrt{1-a^2 x^2}}\\ &=\frac{231 c^2 \sqrt [4]{1-a x} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (1-a x)^{5/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{1}{1-\sqrt{2} x+x^2} \, dx,x,\frac{\sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{1024 a \sqrt{1-a^2 x^2}}-\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{1}{1+\sqrt{2} x+x^2} \, dx,x,\frac{\sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{1024 a \sqrt{1-a^2 x^2}}+\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{\sqrt{2}+2 x}{-1-\sqrt{2} x-x^2} \, dx,x,\frac{\sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}+\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{\sqrt{2}-2 x}{-1+\sqrt{2} x-x^2} \, dx,x,\frac{\sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}\\ &=\frac{231 c^2 \sqrt [4]{1-a x} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (1-a x)^{5/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left (1+\frac{\sqrt{1-a x}}{\sqrt{1+a x}}-\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left (1+\frac{\sqrt{1-a x}}{\sqrt{1+a x}}+\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{1}{-1-x^2} \, dx,x,1-\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{512 \sqrt{2} a \sqrt{1-a^2 x^2}}+\frac{\left (231 c^2 \sqrt{c-a^2 c x^2}\right ) \operatorname{Subst}\left (\int \frac{1}{-1-x^2} \, dx,x,1+\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{512 \sqrt{2} a \sqrt{1-a^2 x^2}}\\ &=\frac{231 c^2 \sqrt [4]{1-a x} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (1-a x)^{5/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (1-a x)^{9/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (1-a x)^{13/4} (1+a x)^{3/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (1-a x)^{13/4} (1+a x)^{7/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^{13/4} (1+a x)^{11/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \tan ^{-1}\left (1-\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{512 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \tan ^{-1}\left (1+\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{512 \sqrt{2} a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left (1+\frac{\sqrt{1-a x}}{\sqrt{1+a x}}-\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left (1+\frac{\sqrt{1-a x}}{\sqrt{1+a x}}+\frac{\sqrt{2} \sqrt [4]{1-a x}}{\sqrt [4]{1+a x}}\right )}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}\\ \end{align*}
Mathematica [C] time = 0.0362318, size = 74, normalized size = 0.11 \[ -\frac{16\ 2^{3/4} c^2 (1-a x)^{13/4} \sqrt{c-a^2 c x^2} \text{Hypergeometric2F1}\left (-\frac{11}{4},\frac{13}{4},\frac{17}{4},\frac{1}{2} (1-a x)\right )}{13 a \sqrt{1-a^2 x^2}} \]
Warning: Unable to verify antiderivative.
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Maple [F] time = 0.198, size = 0, normalized size = 0. \begin{align*} \int \sqrt{{(ax+1){\frac{1}{\sqrt{-{a}^{2}{x}^{2}+1}}}}} \left ( -{a}^{2}c{x}^{2}+c \right ) ^{{\frac{5}{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (-a^{2} c x^{2} + c\right )}^{\frac{5}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (-a^{2} c x^{2} + c\right )}^{\frac{5}{2}} \sqrt{\frac{a x + 1}{\sqrt{-a^{2} x^{2} + 1}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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