Optimal. Leaf size=380 \[ \frac {9 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \sqrt {a+b \text {ArcSin}(c+d x)}}{64 d}+\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \text {ArcSin}(c+d x)}}{32 d}-\frac {3 e^3 (a+b \text {ArcSin}(c+d x))^{3/2}}{32 d}+\frac {e^3 (c+d x)^4 (a+b \text {ArcSin}(c+d x))^{3/2}}{4 d}+\frac {3 b^{3/2} e^3 \sqrt {\frac {\pi }{2}} \cos \left (\frac {4 a}{b}\right ) S\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \text {ArcSin}(c+d x)}}{\sqrt {b}}\right )}{512 d}-\frac {3 b^{3/2} e^3 \sqrt {\pi } \cos \left (\frac {2 a}{b}\right ) S\left (\frac {2 \sqrt {a+b \text {ArcSin}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{64 d}+\frac {3 b^{3/2} e^3 \sqrt {\pi } \text {FresnelC}\left (\frac {2 \sqrt {a+b \text {ArcSin}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right ) \sin \left (\frac {2 a}{b}\right )}{64 d}-\frac {3 b^{3/2} e^3 \sqrt {\frac {\pi }{2}} \text {FresnelC}\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \text {ArcSin}(c+d x)}}{\sqrt {b}}\right ) \sin \left (\frac {4 a}{b}\right )}{512 d} \]
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Rubi [A]
time = 0.69, antiderivative size = 380, normalized size of antiderivative = 1.00, number of steps
used = 27, number of rules used = 12, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.480, Rules used = {4889, 12,
4725, 4795, 4737, 4731, 4491, 3387, 3386, 3432, 3385, 3433} \begin {gather*} \frac {3 \sqrt {\pi } b^{3/2} e^3 \sin \left (\frac {2 a}{b}\right ) \text {FresnelC}\left (\frac {2 \sqrt {a+b \text {ArcSin}(c+d x)}}{\sqrt {\pi } \sqrt {b}}\right )}{64 d}-\frac {3 \sqrt {\frac {\pi }{2}} b^{3/2} e^3 \sin \left (\frac {4 a}{b}\right ) \text {FresnelC}\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \text {ArcSin}(c+d x)}}{\sqrt {b}}\right )}{512 d}+\frac {3 \sqrt {\frac {\pi }{2}} b^{3/2} e^3 \cos \left (\frac {4 a}{b}\right ) S\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \text {ArcSin}(c+d x)}}{\sqrt {b}}\right )}{512 d}-\frac {3 \sqrt {\pi } b^{3/2} e^3 \cos \left (\frac {2 a}{b}\right ) S\left (\frac {2 \sqrt {a+b \text {ArcSin}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{64 d}+\frac {e^3 (c+d x)^4 (a+b \text {ArcSin}(c+d x))^{3/2}}{4 d}+\frac {3 b e^3 \sqrt {1-(c+d x)^2} (c+d x)^3 \sqrt {a+b \text {ArcSin}(c+d x)}}{32 d}+\frac {9 b e^3 \sqrt {1-(c+d x)^2} (c+d x) \sqrt {a+b \text {ArcSin}(c+d x)}}{64 d}-\frac {3 e^3 (a+b \text {ArcSin}(c+d x))^{3/2}}{32 d} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 3385
Rule 3386
Rule 3387
Rule 3432
Rule 3433
Rule 4491
Rule 4725
Rule 4731
Rule 4737
Rule 4795
Rule 4889
Rubi steps
\begin {align*} \int (c e+d e x)^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2} \, dx &=\frac {\text {Subst}\left (\int e^3 x^3 \left (a+b \sin ^{-1}(x)\right )^{3/2} \, dx,x,c+d x\right )}{d}\\ &=\frac {e^3 \text {Subst}\left (\int x^3 \left (a+b \sin ^{-1}(x)\right )^{3/2} \, dx,x,c+d x\right )}{d}\\ &=\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}-\frac {\left (3 b e^3\right ) \text {Subst}\left (\int \frac {x^4 \sqrt {a+b \sin ^{-1}(x)}}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{8 d}\\ &=\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}-\frac {\left (9 b e^3\right ) \text {Subst}\left (\int \frac {x^2 \sqrt {a+b \sin ^{-1}(x)}}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{32 d}-\frac {\left (3 b^2 e^3\right ) \text {Subst}\left (\int \frac {x^3}{\sqrt {a+b \sin ^{-1}(x)}} \, dx,x,c+d x\right )}{64 d}\\ &=\frac {9 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{64 d}+\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}-\frac {\left (9 b e^3\right ) \text {Subst}\left (\int \frac {\sqrt {a+b \sin ^{-1}(x)}}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{64 d}-\frac {\left (3 b^2 e^3\right ) \text {Subst}\left (\int \frac {\cos (x) \sin ^3(x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{64 d}-\frac {\left (9 b^2 e^3\right ) \text {Subst}\left (\int \frac {x}{\sqrt {a+b \sin ^{-1}(x)}} \, dx,x,c+d x\right )}{128 d}\\ &=\frac {9 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{64 d}+\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}-\frac {\left (3 b^2 e^3\right ) \text {Subst}\left (\int \left (\frac {\sin (2 x)}{4 \sqrt {a+b x}}-\frac {\sin (4 x)}{8 \sqrt {a+b x}}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{64 d}-\frac {\left (9 b^2 e^3\right ) \text {Subst}\left (\int \frac {\cos (x) \sin (x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{128 d}\\ &=\frac {9 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{64 d}+\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}+\frac {\left (3 b^2 e^3\right ) \text {Subst}\left (\int \frac {\sin (4 x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{512 d}-\frac {\left (3 b^2 e^3\right ) \text {Subst}\left (\int \frac {\sin (2 x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{256 d}-\frac {\left (9 b^2 e^3\right ) \text {Subst}\left (\int \frac {\sin (2 x)}{2 \sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{128 d}\\ &=\frac {9 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{64 d}+\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}-\frac {\left (9 b^2 e^3\right ) \text {Subst}\left (\int \frac {\sin (2 x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{256 d}-\frac {\left (3 b^2 e^3 \cos \left (\frac {2 a}{b}\right )\right ) \text {Subst}\left (\int \frac {\sin \left (\frac {2 a}{b}+2 x\right )}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{256 d}+\frac {\left (3 b^2 e^3 \cos \left (\frac {4 a}{b}\right )\right ) \text {Subst}\left (\int \frac {\sin \left (\frac {4 a}{b}+4 x\right )}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{512 d}+\frac {\left (3 b^2 e^3 \sin \left (\frac {2 a}{b}\right )\right ) \text {Subst}\left (\int \frac {\cos \left (\frac {2 a}{b}+2 x\right )}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{256 d}-\frac {\left (3 b^2 e^3 \sin \left (\frac {4 a}{b}\right )\right ) \text {Subst}\left (\int \frac {\cos \left (\frac {4 a}{b}+4 x\right )}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{512 d}\\ &=\frac {9 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{64 d}+\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}-\frac {\left (3 b e^3 \cos \left (\frac {2 a}{b}\right )\right ) \text {Subst}\left (\int \sin \left (\frac {2 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{128 d}-\frac {\left (9 b^2 e^3 \cos \left (\frac {2 a}{b}\right )\right ) \text {Subst}\left (\int \frac {\sin \left (\frac {2 a}{b}+2 x\right )}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{256 d}+\frac {\left (3 b e^3 \cos \left (\frac {4 a}{b}\right )\right ) \text {Subst}\left (\int \sin \left (\frac {4 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{256 d}+\frac {\left (3 b e^3 \sin \left (\frac {2 a}{b}\right )\right ) \text {Subst}\left (\int \cos \left (\frac {2 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{128 d}+\frac {\left (9 b^2 e^3 \sin \left (\frac {2 a}{b}\right )\right ) \text {Subst}\left (\int \frac {\cos \left (\frac {2 a}{b}+2 x\right )}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{256 d}-\frac {\left (3 b e^3 \sin \left (\frac {4 a}{b}\right )\right ) \text {Subst}\left (\int \cos \left (\frac {4 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{256 d}\\ &=\frac {9 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{64 d}+\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}+\frac {3 b^{3/2} e^3 \sqrt {\frac {\pi }{2}} \cos \left (\frac {4 a}{b}\right ) S\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right )}{512 d}-\frac {3 b^{3/2} e^3 \sqrt {\pi } \cos \left (\frac {2 a}{b}\right ) S\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{256 d}+\frac {3 b^{3/2} e^3 \sqrt {\pi } C\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right ) \sin \left (\frac {2 a}{b}\right )}{256 d}-\frac {3 b^{3/2} e^3 \sqrt {\frac {\pi }{2}} C\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right ) \sin \left (\frac {4 a}{b}\right )}{512 d}-\frac {\left (9 b e^3 \cos \left (\frac {2 a}{b}\right )\right ) \text {Subst}\left (\int \sin \left (\frac {2 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{128 d}+\frac {\left (9 b e^3 \sin \left (\frac {2 a}{b}\right )\right ) \text {Subst}\left (\int \cos \left (\frac {2 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{128 d}\\ &=\frac {9 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{64 d}+\frac {3 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \sqrt {a+b \sin ^{-1}(c+d x)}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{4 d}+\frac {3 b^{3/2} e^3 \sqrt {\frac {\pi }{2}} \cos \left (\frac {4 a}{b}\right ) S\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right )}{512 d}-\frac {3 b^{3/2} e^3 \sqrt {\pi } \cos \left (\frac {2 a}{b}\right ) S\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{64 d}+\frac {3 b^{3/2} e^3 \sqrt {\pi } C\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right ) \sin \left (\frac {2 a}{b}\right )}{64 d}-\frac {3 b^{3/2} e^3 \sqrt {\frac {\pi }{2}} C\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right ) \sin \left (\frac {4 a}{b}\right )}{512 d}\\ \end {align*}
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Mathematica [C] Result contains complex when optimal does not.
time = 0.13, size = 273, normalized size = 0.72 \begin {gather*} -\frac {i b e^3 e^{-\frac {4 i a}{b}} \sqrt {a+b \text {ArcSin}(c+d x)} \left (8 \sqrt {2} e^{\frac {2 i a}{b}} \sqrt {\frac {i (a+b \text {ArcSin}(c+d x))}{b}} \text {Gamma}\left (\frac {5}{2},-\frac {2 i (a+b \text {ArcSin}(c+d x))}{b}\right )-8 \sqrt {2} e^{\frac {6 i a}{b}} \sqrt {-\frac {i (a+b \text {ArcSin}(c+d x))}{b}} \text {Gamma}\left (\frac {5}{2},\frac {2 i (a+b \text {ArcSin}(c+d x))}{b}\right )-\sqrt {\frac {i (a+b \text {ArcSin}(c+d x))}{b}} \text {Gamma}\left (\frac {5}{2},-\frac {4 i (a+b \text {ArcSin}(c+d x))}{b}\right )+e^{\frac {8 i a}{b}} \sqrt {-\frac {i (a+b \text {ArcSin}(c+d x))}{b}} \text {Gamma}\left (\frac {5}{2},\frac {4 i (a+b \text {ArcSin}(c+d x))}{b}\right )\right )}{512 d \sqrt {\frac {(a+b \text {ArcSin}(c+d x))^2}{b^2}}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.50, size = 610, normalized size = 1.61
method | result | size |
default | \(-\frac {e^{3} \left (3 \sqrt {-\frac {1}{b}}\, \sqrt {\pi }\, \sqrt {2}\, \sqrt {a +b \arcsin \left (d x +c \right )}\, \cos \left (\frac {4 a}{b}\right ) \mathrm {S}\left (\frac {2 \sqrt {2}\, \sqrt {a +b \arcsin \left (d x +c \right )}}{\sqrt {\pi }\, \sqrt {-\frac {1}{b}}\, b}\right ) b^{2}+3 \sqrt {-\frac {1}{b}}\, \sqrt {\pi }\, \sqrt {2}\, \sqrt {a +b \arcsin \left (d x +c \right )}\, \sin \left (\frac {4 a}{b}\right ) \FresnelC \left (\frac {2 \sqrt {2}\, \sqrt {a +b \arcsin \left (d x +c \right )}}{\sqrt {\pi }\, \sqrt {-\frac {1}{b}}\, b}\right ) b^{2}-24 \sqrt {-\frac {2}{b}}\, \sqrt {\pi }\, \sqrt {2}\, \sqrt {a +b \arcsin \left (d x +c \right )}\, \cos \left (\frac {2 a}{b}\right ) \mathrm {S}\left (\frac {2 \sqrt {2}\, \sqrt {a +b \arcsin \left (d x +c \right )}}{\sqrt {\pi }\, \sqrt {-\frac {2}{b}}\, b}\right ) b^{2}-24 \sqrt {-\frac {2}{b}}\, \sqrt {\pi }\, \sqrt {2}\, \sqrt {a +b \arcsin \left (d x +c \right )}\, \sin \left (\frac {2 a}{b}\right ) \FresnelC \left (\frac {2 \sqrt {2}\, \sqrt {a +b \arcsin \left (d x +c \right )}}{\sqrt {\pi }\, \sqrt {-\frac {2}{b}}\, b}\right ) b^{2}+128 \arcsin \left (d x +c \right )^{2} \cos \left (-\frac {2 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {2 a}{b}\right ) b^{2}-32 \arcsin \left (d x +c \right )^{2} \cos \left (-\frac {4 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {4 a}{b}\right ) b^{2}+256 \arcsin \left (d x +c \right ) \cos \left (-\frac {2 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {2 a}{b}\right ) a b +96 \arcsin \left (d x +c \right ) \sin \left (-\frac {2 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {2 a}{b}\right ) b^{2}-64 \arcsin \left (d x +c \right ) \cos \left (-\frac {4 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {4 a}{b}\right ) a b -12 \arcsin \left (d x +c \right ) \sin \left (-\frac {4 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {4 a}{b}\right ) b^{2}+128 \cos \left (-\frac {2 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {2 a}{b}\right ) a^{2}+96 \sin \left (-\frac {2 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {2 a}{b}\right ) a b -32 \cos \left (-\frac {4 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {4 a}{b}\right ) a^{2}-12 \sin \left (-\frac {4 \left (a +b \arcsin \left (d x +c \right )\right )}{b}+\frac {4 a}{b}\right ) a b \right )}{1024 d \sqrt {a +b \arcsin \left (d x +c \right )}}\) | \(610\) |
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(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \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*} e^{3} \left (\int a c^{3} \sqrt {a + b \operatorname {asin}{\left (c + d x \right )}}\, dx + \int a d^{3} x^{3} \sqrt {a + b \operatorname {asin}{\left (c + d x \right )}}\, dx + \int b c^{3} \sqrt {a + b \operatorname {asin}{\left (c + d x \right )}} \operatorname {asin}{\left (c + d x \right )}\, dx + \int 3 a c d^{2} x^{2} \sqrt {a + b \operatorname {asin}{\left (c + d x \right )}}\, dx + \int 3 a c^{2} d x \sqrt {a + b \operatorname {asin}{\left (c + d x \right )}}\, dx + \int b d^{3} x^{3} \sqrt {a + b \operatorname {asin}{\left (c + d x \right )}} \operatorname {asin}{\left (c + d x \right )}\, dx + \int 3 b c d^{2} x^{2} \sqrt {a + b \operatorname {asin}{\left (c + d x \right )}} \operatorname {asin}{\left (c + d x \right )}\, dx + \int 3 b c^{2} d x \sqrt {a + b \operatorname {asin}{\left (c + d x \right )}} \operatorname {asin}{\left (c + d x \right )}\, dx\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [C] Result contains complex when optimal does not.
time = 1.29, size = 2237, normalized size = 5.89 \begin {gather*} \text {Too large to display} \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 {\left (c\,e+d\,e\,x\right )}^3\,{\left (a+b\,\mathrm {asin}\left (c+d\,x\right )\right )}^{3/2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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