Optimal. Leaf size=475 \[ \frac {15 \sqrt {\frac {\pi }{2}} b^{5/2} e^3 \cos \left (\frac {4 a}{b}\right ) C\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right )}{4096 d}-\frac {15 \sqrt {\pi } b^{5/2} e^3 \cos \left (\frac {2 a}{b}\right ) C\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{256 d}-\frac {15 \sqrt {\pi } b^{5/2} e^3 \sin \left (\frac {2 a}{b}\right ) S\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{256 d}+\frac {15 \sqrt {\frac {\pi }{2}} b^{5/2} e^3 \sin \left (\frac {4 a}{b}\right ) S\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right )}{4096 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {225 b^2 e^3 \sqrt {a+b \sin ^{-1}(c+d x)}}{2048 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}+\frac {5 b e^3 \sqrt {1-(c+d x)^2} (c+d x)^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}+\frac {15 b e^3 \sqrt {1-(c+d x)^2} (c+d x) \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d} \]
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Rubi [A] time = 1.60, antiderivative size = 475, normalized size of antiderivative = 1.00, number of steps used = 29, number of rules used = 12, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.480, Rules used = {4805, 12, 4629, 4707, 4641, 4723, 3312, 3306, 3305, 3351, 3304, 3352} \[ \frac {15 \sqrt {\frac {\pi }{2}} b^{5/2} e^3 \cos \left (\frac {4 a}{b}\right ) \text {FresnelC}\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right )}{4096 d}-\frac {15 \sqrt {\pi } b^{5/2} e^3 \cos \left (\frac {2 a}{b}\right ) \text {FresnelC}\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {\pi } \sqrt {b}}\right )}{256 d}-\frac {15 \sqrt {\pi } b^{5/2} e^3 \sin \left (\frac {2 a}{b}\right ) S\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{256 d}+\frac {15 \sqrt {\frac {\pi }{2}} b^{5/2} e^3 \sin \left (\frac {4 a}{b}\right ) S\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right )}{4096 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {225 b^2 e^3 \sqrt {a+b \sin ^{-1}(c+d x)}}{2048 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}+\frac {5 b e^3 \sqrt {1-(c+d x)^2} (c+d x)^3 \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}+\frac {15 b e^3 \sqrt {1-(c+d x)^2} (c+d x) \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d} \]
Antiderivative was successfully verified.
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Rule 12
Rule 3304
Rule 3305
Rule 3306
Rule 3312
Rule 3351
Rule 3352
Rule 4629
Rule 4641
Rule 4707
Rule 4723
Rule 4805
Rubi steps
\begin {align*} \int (c e+d e x)^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2} \, dx &=\frac {\operatorname {Subst}\left (\int e^3 x^3 \left (a+b \sin ^{-1}(x)\right )^{5/2} \, dx,x,c+d x\right )}{d}\\ &=\frac {e^3 \operatorname {Subst}\left (\int x^3 \left (a+b \sin ^{-1}(x)\right )^{5/2} \, dx,x,c+d x\right )}{d}\\ &=\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}-\frac {\left (5 b e^3\right ) \operatorname {Subst}\left (\int \frac {x^4 \left (a+b \sin ^{-1}(x)\right )^{3/2}}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{8 d}\\ &=\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \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 )^{5/2}}{4 d}-\frac {\left (15 b e^3\right ) \operatorname {Subst}\left (\int \frac {x^2 \left (a+b \sin ^{-1}(x)\right )^{3/2}}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{32 d}-\frac {\left (15 b^2 e^3\right ) \operatorname {Subst}\left (\int x^3 \sqrt {a+b \sin ^{-1}(x)} \, dx,x,c+d x\right )}{64 d}\\ &=-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {15 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}+\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \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 )^{5/2}}{4 d}-\frac {\left (15 b e^3\right ) \operatorname {Subst}\left (\int \frac {\left (a+b \sin ^{-1}(x)\right )^{3/2}}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{64 d}-\frac {\left (45 b^2 e^3\right ) \operatorname {Subst}\left (\int x \sqrt {a+b \sin ^{-1}(x)} \, dx,x,c+d x\right )}{128 d}+\frac {\left (15 b^3 e^3\right ) \operatorname {Subst}\left (\int \frac {x^4}{\sqrt {1-x^2} \sqrt {a+b \sin ^{-1}(x)}} \, dx,x,c+d x\right )}{512 d}\\ &=-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {15 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}+\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}+\frac {\left (15 b^3 e^3\right ) \operatorname {Subst}\left (\int \frac {\sin ^4(x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{512 d}+\frac {\left (45 b^3 e^3\right ) \operatorname {Subst}\left (\int \frac {x^2}{\sqrt {1-x^2} \sqrt {a+b \sin ^{-1}(x)}} \, dx,x,c+d x\right )}{512 d}\\ &=-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {15 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}+\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}+\frac {\left (15 b^3 e^3\right ) \operatorname {Subst}\left (\int \left (\frac {3}{8 \sqrt {a+b x}}-\frac {\cos (2 x)}{2 \sqrt {a+b x}}+\frac {\cos (4 x)}{8 \sqrt {a+b x}}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{512 d}+\frac {\left (45 b^3 e^3\right ) \operatorname {Subst}\left (\int \frac {\sin ^2(x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{512 d}\\ &=\frac {45 b^2 e^3 \sqrt {a+b \sin ^{-1}(c+d x)}}{2048 d}-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {15 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}+\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}+\frac {\left (15 b^3 e^3\right ) \operatorname {Subst}\left (\int \frac {\cos (4 x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{4096 d}-\frac {\left (15 b^3 e^3\right ) \operatorname {Subst}\left (\int \frac {\cos (2 x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{1024 d}+\frac {\left (45 b^3 e^3\right ) \operatorname {Subst}\left (\int \left (\frac {1}{2 \sqrt {a+b x}}-\frac {\cos (2 x)}{2 \sqrt {a+b x}}\right ) \, dx,x,\sin ^{-1}(c+d x)\right )}{512 d}\\ &=\frac {225 b^2 e^3 \sqrt {a+b \sin ^{-1}(c+d x)}}{2048 d}-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {15 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}+\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}-\frac {\left (45 b^3 e^3\right ) \operatorname {Subst}\left (\int \frac {\cos (2 x)}{\sqrt {a+b x}} \, dx,x,\sin ^{-1}(c+d x)\right )}{1024 d}-\frac {\left (15 b^3 e^3 \cos \left (\frac {2 a}{b}\right )\right ) \operatorname {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 )}{1024 d}+\frac {\left (15 b^3 e^3 \cos \left (\frac {4 a}{b}\right )\right ) \operatorname {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 )}{4096 d}-\frac {\left (15 b^3 e^3 \sin \left (\frac {2 a}{b}\right )\right ) \operatorname {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 )}{1024 d}+\frac {\left (15 b^3 e^3 \sin \left (\frac {4 a}{b}\right )\right ) \operatorname {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 )}{4096 d}\\ &=\frac {225 b^2 e^3 \sqrt {a+b \sin ^{-1}(c+d x)}}{2048 d}-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {15 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}+\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}-\frac {\left (15 b^2 e^3 \cos \left (\frac {2 a}{b}\right )\right ) \operatorname {Subst}\left (\int \cos \left (\frac {2 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{512 d}-\frac {\left (45 b^3 e^3 \cos \left (\frac {2 a}{b}\right )\right ) \operatorname {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 )}{1024 d}+\frac {\left (15 b^2 e^3 \cos \left (\frac {4 a}{b}\right )\right ) \operatorname {Subst}\left (\int \cos \left (\frac {4 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{2048 d}-\frac {\left (15 b^2 e^3 \sin \left (\frac {2 a}{b}\right )\right ) \operatorname {Subst}\left (\int \sin \left (\frac {2 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{512 d}-\frac {\left (45 b^3 e^3 \sin \left (\frac {2 a}{b}\right )\right ) \operatorname {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 )}{1024 d}+\frac {\left (15 b^2 e^3 \sin \left (\frac {4 a}{b}\right )\right ) \operatorname {Subst}\left (\int \sin \left (\frac {4 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{2048 d}\\ &=\frac {225 b^2 e^3 \sqrt {a+b \sin ^{-1}(c+d x)}}{2048 d}-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {15 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}+\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}+\frac {15 b^{5/2} e^3 \sqrt {\frac {\pi }{2}} \cos \left (\frac {4 a}{b}\right ) C\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right )}{4096 d}-\frac {15 b^{5/2} e^3 \sqrt {\pi } \cos \left (\frac {2 a}{b}\right ) C\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{1024 d}-\frac {15 b^{5/2} e^3 \sqrt {\pi } S\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right ) \sin \left (\frac {2 a}{b}\right )}{1024 d}+\frac {15 b^{5/2} e^3 \sqrt {\frac {\pi }{2}} S\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 )}{4096 d}-\frac {\left (45 b^2 e^3 \cos \left (\frac {2 a}{b}\right )\right ) \operatorname {Subst}\left (\int \cos \left (\frac {2 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{512 d}-\frac {\left (45 b^2 e^3 \sin \left (\frac {2 a}{b}\right )\right ) \operatorname {Subst}\left (\int \sin \left (\frac {2 x^2}{b}\right ) \, dx,x,\sqrt {a+b \sin ^{-1}(c+d x)}\right )}{512 d}\\ &=\frac {225 b^2 e^3 \sqrt {a+b \sin ^{-1}(c+d x)}}{2048 d}-\frac {45 b^2 e^3 (c+d x)^2 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}-\frac {15 b^2 e^3 (c+d x)^4 \sqrt {a+b \sin ^{-1}(c+d x)}}{256 d}+\frac {15 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{64 d}+\frac {5 b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^{3/2}}{32 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^{5/2}}{4 d}+\frac {15 b^{5/2} e^3 \sqrt {\frac {\pi }{2}} \cos \left (\frac {4 a}{b}\right ) C\left (\frac {2 \sqrt {\frac {2}{\pi }} \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b}}\right )}{4096 d}-\frac {15 b^{5/2} e^3 \sqrt {\pi } \cos \left (\frac {2 a}{b}\right ) C\left (\frac {2 \sqrt {a+b \sin ^{-1}(c+d x)}}{\sqrt {b} \sqrt {\pi }}\right )}{256 d}-\frac {15 b^{5/2} e^3 \sqrt {\pi } S\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 {15 b^{5/2} e^3 \sqrt {\frac {\pi }{2}} S\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 )}{4096 d}\\ \end {align*}
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Mathematica [C] time = 0.32, size = 269, normalized size = 0.57 \[ -\frac {e^3 e^{-\frac {4 i a}{b}} \left (a+b \sin ^{-1}(c+d x)\right )^{5/2} \left (-16 \sqrt {2} e^{\frac {2 i a}{b}} \sqrt {\frac {i \left (a+b \sin ^{-1}(c+d x)\right )}{b}} \Gamma \left (\frac {7}{2},-\frac {2 i \left (a+b \sin ^{-1}(c+d x)\right )}{b}\right )-16 \sqrt {2} e^{\frac {6 i a}{b}} \sqrt {-\frac {i \left (a+b \sin ^{-1}(c+d x)\right )}{b}} \Gamma \left (\frac {7}{2},\frac {2 i \left (a+b \sin ^{-1}(c+d x)\right )}{b}\right )+\sqrt {\frac {i \left (a+b \sin ^{-1}(c+d x)\right )}{b}} \Gamma \left (\frac {7}{2},-\frac {4 i \left (a+b \sin ^{-1}(c+d x)\right )}{b}\right )+e^{\frac {8 i a}{b}} \sqrt {-\frac {i \left (a+b \sin ^{-1}(c+d x)\right )}{b}} \Gamma \left (\frac {7}{2},\frac {4 i \left (a+b \sin ^{-1}(c+d x)\right )}{b}\right )\right )}{2048 d \left (\frac {\left (a+b \sin ^{-1}(c+d x)\right )^2}{b^2}\right )^{3/2}} \]
Warning: Unable to verify antiderivative.
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fricas [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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giac [B] time = 3.57, size = 3439, normalized size = 7.24 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.39, size = 864, normalized size = 1.82 \[ \text {result too large to display} \]
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 \[ \int {\left (d e x + c e\right )}^{3} {\left (b \arcsin \left (d x + c\right ) + a\right )}^{\frac {5}{2}}\,{d x} \]
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 \[ \int {\left (c\,e+d\,e\,x\right )}^3\,{\left (a+b\,\mathrm {asin}\left (c+d\,x\right )\right )}^{5/2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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