Optimal. Leaf size=754 \[ \text{result too large to display} \]
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Rubi [A] time = 2.26488, antiderivative size = 754, normalized size of antiderivative = 1., number of steps used = 42, number of rules used = 10, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.454, Rules used = {4667, 4619, 4723, 3306, 3305, 3351, 3304, 3352, 4629, 3312} \[ \frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d e \sin \left (\frac{a}{b}\right ) \text{FresnelC}\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{2 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} d e \sin \left (\frac{3 a}{b}\right ) \text{FresnelC}\left (\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{6 c^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d e \cos \left (\frac{a}{b}\right ) S\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{2 c^3}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} d e \cos \left (\frac{3 a}{b}\right ) S\left (\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{6 c^3}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^2 \sin \left (\frac{a}{b}\right ) \text{FresnelC}\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{8 c^5}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e^2 \sin \left (\frac{3 a}{b}\right ) \text{FresnelC}\left (\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{16 c^5}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{b} e^2 \sin \left (\frac{5 a}{b}\right ) \text{FresnelC}\left (\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{80 c^5}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^2 \cos \left (\frac{a}{b}\right ) S\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{8 c^5}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e^2 \cos \left (\frac{3 a}{b}\right ) S\left (\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{16 c^5}-\frac{\sqrt{\frac{\pi }{10}} \sqrt{b} e^2 \cos \left (\frac{5 a}{b}\right ) S\left (\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{80 c^5}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d^2 \sin \left (\frac{a}{b}\right ) \text{FresnelC}\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d^2 \cos \left (\frac{a}{b}\right ) S\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{c}+d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)} \]
Antiderivative was successfully verified.
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Rule 4667
Rule 4619
Rule 4723
Rule 3306
Rule 3305
Rule 3351
Rule 3304
Rule 3352
Rule 4629
Rule 3312
Rubi steps
\begin{align*} \int \left (d+e x^2\right )^2 \sqrt{a+b \sin ^{-1}(c x)} \, dx &=\int \left (d^2 \sqrt{a+b \sin ^{-1}(c x)}+2 d e x^2 \sqrt{a+b \sin ^{-1}(c x)}+e^2 x^4 \sqrt{a+b \sin ^{-1}(c x)}\right ) \, dx\\ &=d^2 \int \sqrt{a+b \sin ^{-1}(c x)} \, dx+(2 d e) \int x^2 \sqrt{a+b \sin ^{-1}(c x)} \, dx+e^2 \int x^4 \sqrt{a+b \sin ^{-1}(c x)} \, dx\\ &=d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}-\frac{1}{2} \left (b c d^2\right ) \int \frac{x}{\sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}} \, dx-\frac{1}{3} (b c d e) \int \frac{x^3}{\sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}} \, dx-\frac{1}{10} \left (b c e^2\right ) \int \frac{x^5}{\sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}} \, dx\\ &=d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}-\frac{\left (b d^2\right ) \operatorname{Subst}\left (\int \frac{\sin (x)}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{2 c}-\frac{(b d e) \operatorname{Subst}\left (\int \frac{\sin ^3(x)}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{3 c^3}-\frac{\left (b e^2\right ) \operatorname{Subst}\left (\int \frac{\sin ^5(x)}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{10 c^5}\\ &=d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}-\frac{(b d e) \operatorname{Subst}\left (\int \left (\frac{3 \sin (x)}{4 \sqrt{a+b x}}-\frac{\sin (3 x)}{4 \sqrt{a+b x}}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{3 c^3}-\frac{\left (b e^2\right ) \operatorname{Subst}\left (\int \left (\frac{5 \sin (x)}{8 \sqrt{a+b x}}-\frac{5 \sin (3 x)}{16 \sqrt{a+b x}}+\frac{\sin (5 x)}{16 \sqrt{a+b x}}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{10 c^5}-\frac{\left (b d^2 \cos \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\sin \left (\frac{a}{b}+x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{2 c}+\frac{\left (b d^2 \sin \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\cos \left (\frac{a}{b}+x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{2 c}\\ &=d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}+\frac{(b d e) \operatorname{Subst}\left (\int \frac{\sin (3 x)}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{12 c^3}-\frac{(b d e) \operatorname{Subst}\left (\int \frac{\sin (x)}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{4 c^3}-\frac{\left (b e^2\right ) \operatorname{Subst}\left (\int \frac{\sin (5 x)}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{160 c^5}+\frac{\left (b e^2\right ) \operatorname{Subst}\left (\int \frac{\sin (3 x)}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{32 c^5}-\frac{\left (b e^2\right ) \operatorname{Subst}\left (\int \frac{\sin (x)}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{16 c^5}-\frac{\left (d^2 \cos \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \sin \left (\frac{x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{c}+\frac{\left (d^2 \sin \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \cos \left (\frac{x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{c}\\ &=d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}-\frac{\sqrt{b} d^2 \sqrt{\frac{\pi }{2}} \cos \left (\frac{a}{b}\right ) S\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{c}+\frac{\sqrt{b} d^2 \sqrt{\frac{\pi }{2}} C\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right ) \sin \left (\frac{a}{b}\right )}{c}-\frac{\left (b d e \cos \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\sin \left (\frac{a}{b}+x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{4 c^3}-\frac{\left (b e^2 \cos \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\sin \left (\frac{a}{b}+x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{16 c^5}+\frac{\left (b d e \cos \left (\frac{3 a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\sin \left (\frac{3 a}{b}+3 x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{12 c^3}+\frac{\left (b e^2 \cos \left (\frac{3 a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\sin \left (\frac{3 a}{b}+3 x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{32 c^5}-\frac{\left (b e^2 \cos \left (\frac{5 a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\sin \left (\frac{5 a}{b}+5 x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{160 c^5}+\frac{\left (b d e \sin \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\cos \left (\frac{a}{b}+x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{4 c^3}+\frac{\left (b e^2 \sin \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\cos \left (\frac{a}{b}+x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{16 c^5}-\frac{\left (b d e \sin \left (\frac{3 a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\cos \left (\frac{3 a}{b}+3 x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{12 c^3}-\frac{\left (b e^2 \sin \left (\frac{3 a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\cos \left (\frac{3 a}{b}+3 x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{32 c^5}+\frac{\left (b e^2 \sin \left (\frac{5 a}{b}\right )\right ) \operatorname{Subst}\left (\int \frac{\cos \left (\frac{5 a}{b}+5 x\right )}{\sqrt{a+b x}} \, dx,x,\sin ^{-1}(c x)\right )}{160 c^5}\\ &=d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}-\frac{\sqrt{b} d^2 \sqrt{\frac{\pi }{2}} \cos \left (\frac{a}{b}\right ) S\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{c}+\frac{\sqrt{b} d^2 \sqrt{\frac{\pi }{2}} C\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right ) \sin \left (\frac{a}{b}\right )}{c}-\frac{\left (d e \cos \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \sin \left (\frac{x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{2 c^3}-\frac{\left (e^2 \cos \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \sin \left (\frac{x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{8 c^5}+\frac{\left (d e \cos \left (\frac{3 a}{b}\right )\right ) \operatorname{Subst}\left (\int \sin \left (\frac{3 x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{6 c^3}+\frac{\left (e^2 \cos \left (\frac{3 a}{b}\right )\right ) \operatorname{Subst}\left (\int \sin \left (\frac{3 x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{16 c^5}-\frac{\left (e^2 \cos \left (\frac{5 a}{b}\right )\right ) \operatorname{Subst}\left (\int \sin \left (\frac{5 x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{80 c^5}+\frac{\left (d e \sin \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \cos \left (\frac{x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{2 c^3}+\frac{\left (e^2 \sin \left (\frac{a}{b}\right )\right ) \operatorname{Subst}\left (\int \cos \left (\frac{x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{8 c^5}-\frac{\left (d e \sin \left (\frac{3 a}{b}\right )\right ) \operatorname{Subst}\left (\int \cos \left (\frac{3 x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{6 c^3}-\frac{\left (e^2 \sin \left (\frac{3 a}{b}\right )\right ) \operatorname{Subst}\left (\int \cos \left (\frac{3 x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{16 c^5}+\frac{\left (e^2 \sin \left (\frac{5 a}{b}\right )\right ) \operatorname{Subst}\left (\int \cos \left (\frac{5 x^2}{b}\right ) \, dx,x,\sqrt{a+b \sin ^{-1}(c x)}\right )}{80 c^5}\\ &=d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}-\frac{\sqrt{b} d^2 \sqrt{\frac{\pi }{2}} \cos \left (\frac{a}{b}\right ) S\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{c}-\frac{\sqrt{b} d e \sqrt{\frac{\pi }{2}} \cos \left (\frac{a}{b}\right ) S\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{2 c^3}-\frac{\sqrt{b} e^2 \sqrt{\frac{\pi }{2}} \cos \left (\frac{a}{b}\right ) S\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{8 c^5}+\frac{\sqrt{b} d e \sqrt{\frac{\pi }{6}} \cos \left (\frac{3 a}{b}\right ) S\left (\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{6 c^3}+\frac{\sqrt{b} e^2 \sqrt{\frac{\pi }{6}} \cos \left (\frac{3 a}{b}\right ) S\left (\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{16 c^5}-\frac{\sqrt{b} e^2 \sqrt{\frac{\pi }{10}} \cos \left (\frac{5 a}{b}\right ) S\left (\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right )}{80 c^5}+\frac{\sqrt{b} d^2 \sqrt{\frac{\pi }{2}} C\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right ) \sin \left (\frac{a}{b}\right )}{c}+\frac{\sqrt{b} d e \sqrt{\frac{\pi }{2}} C\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right ) \sin \left (\frac{a}{b}\right )}{2 c^3}+\frac{\sqrt{b} e^2 \sqrt{\frac{\pi }{2}} C\left (\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right ) \sin \left (\frac{a}{b}\right )}{8 c^5}-\frac{\sqrt{b} d e \sqrt{\frac{\pi }{6}} C\left (\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right ) \sin \left (\frac{3 a}{b}\right )}{6 c^3}-\frac{\sqrt{b} e^2 \sqrt{\frac{\pi }{6}} C\left (\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right ) \sin \left (\frac{3 a}{b}\right )}{16 c^5}+\frac{\sqrt{b} e^2 \sqrt{\frac{\pi }{10}} C\left (\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right ) \sin \left (\frac{5 a}{b}\right )}{80 c^5}\\ \end{align*}
Mathematica [C] time = 1.56011, size = 400, normalized size = 0.53 \[ \frac{b e^{-\frac{5 i a}{b}} \left (450 e^{\frac{4 i a}{b}} \left (8 c^4 d^2+4 c^2 d e+e^2\right ) \sqrt{-\frac{i \left (a+b \sin ^{-1}(c x)\right )}{b}} \text{Gamma}\left (\frac{3}{2},-\frac{i \left (a+b \sin ^{-1}(c x)\right )}{b}\right )+450 e^{\frac{6 i a}{b}} \left (8 c^4 d^2+4 c^2 d e+e^2\right ) \sqrt{\frac{i \left (a+b \sin ^{-1}(c x)\right )}{b}} \text{Gamma}\left (\frac{3}{2},\frac{i \left (a+b \sin ^{-1}(c x)\right )}{b}\right )-e \left (25 \sqrt{3} e^{\frac{2 i a}{b}} \left (8 c^2 d+3 e\right ) \sqrt{-\frac{i \left (a+b \sin ^{-1}(c x)\right )}{b}} \text{Gamma}\left (\frac{3}{2},-\frac{3 i \left (a+b \sin ^{-1}(c x)\right )}{b}\right )+25 \sqrt{3} e^{\frac{8 i a}{b}} \left (8 c^2 d+3 e\right ) \sqrt{\frac{i \left (a+b \sin ^{-1}(c x)\right )}{b}} \text{Gamma}\left (\frac{3}{2},\frac{3 i \left (a+b \sin ^{-1}(c x)\right )}{b}\right )-9 \sqrt{5} e \left (\sqrt{-\frac{i \left (a+b \sin ^{-1}(c x)\right )}{b}} \text{Gamma}\left (\frac{3}{2},-\frac{5 i \left (a+b \sin ^{-1}(c x)\right )}{b}\right )+e^{\frac{10 i a}{b}} \sqrt{\frac{i \left (a+b \sin ^{-1}(c x)\right )}{b}} \text{Gamma}\left (\frac{3}{2},\frac{5 i \left (a+b \sin ^{-1}(c x)\right )}{b}\right )\right )\right )\right )}{7200 c^5 \sqrt{a+b \sin ^{-1}(c x)}} \]
Warning: Unable to verify antiderivative.
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Maple [A] time = 0.159, size = 1137, normalized size = 1.5 \begin{align*} \text{result too large to display} \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 (e x^{2} + d\right )}^{2} \sqrt{b \arcsin \left (c x\right ) + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{a + b \operatorname{asin}{\left (c x \right )}} \left (d + e x^{2}\right )^{2}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [C] time = 3.21901, size = 1751, normalized size = 2.32 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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