Optimal. Leaf size=357 \[ \frac {45 b^4 e^3 (c+d x)^2}{128 d}+\frac {3 b^4 e^3 (c+d x)^4}{128 d}-\frac {45 b^3 e^3 (c+d x) \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))}{64 d}-\frac {3 b^3 e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))}{32 d}+\frac {45 b^2 e^3 (a+b \text {ArcSin}(c+d x))^2}{128 d}-\frac {9 b^2 e^3 (c+d x)^2 (a+b \text {ArcSin}(c+d x))^2}{16 d}-\frac {3 b^2 e^3 (c+d x)^4 (a+b \text {ArcSin}(c+d x))^2}{16 d}+\frac {3 b e^3 (c+d x) \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))^3}{8 d}+\frac {b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))^3}{4 d}-\frac {3 e^3 (a+b \text {ArcSin}(c+d x))^4}{32 d}+\frac {e^3 (c+d x)^4 (a+b \text {ArcSin}(c+d x))^4}{4 d} \]
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Rubi [A]
time = 0.44, antiderivative size = 357, normalized size of antiderivative = 1.00, number of steps
used = 16, number of rules used = 6, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.261, Rules used = {4889, 12,
4723, 4795, 4737, 30} \begin {gather*} -\frac {3 b^3 e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))}{32 d}-\frac {45 b^3 e^3 (c+d x) \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))}{64 d}-\frac {3 b^2 e^3 (c+d x)^4 (a+b \text {ArcSin}(c+d x))^2}{16 d}+\frac {45 b^2 e^3 (a+b \text {ArcSin}(c+d x))^2}{128 d}-\frac {9 b^2 e^3 (c+d x)^2 (a+b \text {ArcSin}(c+d x))^2}{16 d}+\frac {b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))^3}{4 d}+\frac {3 b e^3 (c+d x) \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))^3}{8 d}+\frac {e^3 (c+d x)^4 (a+b \text {ArcSin}(c+d x))^4}{4 d}-\frac {3 e^3 (a+b \text {ArcSin}(c+d x))^4}{32 d}+\frac {3 b^4 e^3 (c+d x)^4}{128 d}+\frac {45 b^4 e^3 (c+d x)^2}{128 d} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 4723
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 )^4 \, dx &=\frac {\text {Subst}\left (\int e^3 x^3 \left (a+b \sin ^{-1}(x)\right )^4 \, dx,x,c+d x\right )}{d}\\ &=\frac {e^3 \text {Subst}\left (\int x^3 \left (a+b \sin ^{-1}(x)\right )^4 \, dx,x,c+d x\right )}{d}\\ &=\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^4}{4 d}-\frac {\left (b e^3\right ) \text {Subst}\left (\int \frac {x^4 \left (a+b \sin ^{-1}(x)\right )^3}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{d}\\ &=\frac {b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{4 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^4}{4 d}-\frac {\left (3 b e^3\right ) \text {Subst}\left (\int \frac {x^2 \left (a+b \sin ^{-1}(x)\right )^3}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{4 d}-\frac {\left (3 b^2 e^3\right ) \text {Subst}\left (\int x^3 \left (a+b \sin ^{-1}(x)\right )^2 \, dx,x,c+d x\right )}{4 d}\\ &=-\frac {3 b^2 e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^2}{16 d}+\frac {3 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{8 d}+\frac {b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{4 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^4}{4 d}-\frac {\left (3 b e^3\right ) \text {Subst}\left (\int \frac {\left (a+b \sin ^{-1}(x)\right )^3}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{8 d}-\frac {\left (9 b^2 e^3\right ) \text {Subst}\left (\int x \left (a+b \sin ^{-1}(x)\right )^2 \, dx,x,c+d x\right )}{8 d}+\frac {\left (3 b^3 e^3\right ) \text {Subst}\left (\int \frac {x^4 \left (a+b \sin ^{-1}(x)\right )}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{8 d}\\ &=-\frac {3 b^3 e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )}{32 d}-\frac {9 b^2 e^3 (c+d x)^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{16 d}-\frac {3 b^2 e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^2}{16 d}+\frac {3 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{8 d}+\frac {b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{4 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^4}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^4}{4 d}+\frac {\left (9 b^3 e^3\right ) \text {Subst}\left (\int \frac {x^2 \left (a+b \sin ^{-1}(x)\right )}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{32 d}+\frac {\left (9 b^3 e^3\right ) \text {Subst}\left (\int \frac {x^2 \left (a+b \sin ^{-1}(x)\right )}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{8 d}+\frac {\left (3 b^4 e^3\right ) \text {Subst}\left (\int x^3 \, dx,x,c+d x\right )}{32 d}\\ &=\frac {3 b^4 e^3 (c+d x)^4}{128 d}-\frac {45 b^3 e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )}{64 d}-\frac {3 b^3 e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )}{32 d}-\frac {9 b^2 e^3 (c+d x)^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{16 d}-\frac {3 b^2 e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^2}{16 d}+\frac {3 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{8 d}+\frac {b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{4 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^4}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^4}{4 d}+\frac {\left (9 b^3 e^3\right ) \text {Subst}\left (\int \frac {a+b \sin ^{-1}(x)}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{64 d}+\frac {\left (9 b^3 e^3\right ) \text {Subst}\left (\int \frac {a+b \sin ^{-1}(x)}{\sqrt {1-x^2}} \, dx,x,c+d x\right )}{16 d}+\frac {\left (9 b^4 e^3\right ) \text {Subst}(\int x \, dx,x,c+d x)}{64 d}+\frac {\left (9 b^4 e^3\right ) \text {Subst}(\int x \, dx,x,c+d x)}{16 d}\\ &=\frac {45 b^4 e^3 (c+d x)^2}{128 d}+\frac {3 b^4 e^3 (c+d x)^4}{128 d}-\frac {45 b^3 e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )}{64 d}-\frac {3 b^3 e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )}{32 d}+\frac {45 b^2 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^2}{128 d}-\frac {9 b^2 e^3 (c+d x)^2 \left (a+b \sin ^{-1}(c+d x)\right )^2}{16 d}-\frac {3 b^2 e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^2}{16 d}+\frac {3 b e^3 (c+d x) \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{8 d}+\frac {b e^3 (c+d x)^3 \sqrt {1-(c+d x)^2} \left (a+b \sin ^{-1}(c+d x)\right )^3}{4 d}-\frac {3 e^3 \left (a+b \sin ^{-1}(c+d x)\right )^4}{32 d}+\frac {e^3 (c+d x)^4 \left (a+b \sin ^{-1}(c+d x)\right )^4}{4 d}\\ \end {align*}
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Mathematica [A]
time = 0.33, size = 287, normalized size = 0.80 \begin {gather*} \frac {e^3 \left (\frac {45}{4} b^4 (c+d x)^2+\frac {3}{4} b^4 (c+d x)^4-\frac {45}{2} b^3 (c+d x) \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))-3 b^3 (c+d x)^3 \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))+\frac {45}{4} b^2 (a+b \text {ArcSin}(c+d x))^2-18 b^2 (c+d x)^2 (a+b \text {ArcSin}(c+d x))^2-6 b^2 (c+d x)^4 (a+b \text {ArcSin}(c+d x))^2+12 b (c+d x) \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))^3+8 b (c+d x)^3 \sqrt {1-(c+d x)^2} (a+b \text {ArcSin}(c+d x))^3-3 (a+b \text {ArcSin}(c+d x))^4+8 (c+d x)^4 (a+b \text {ArcSin}(c+d x))^4\right )}{32 d} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(656\) vs.
\(2(327)=654\).
time = 0.12, size = 657, normalized size = 1.84 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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1032 vs.
\(2 (316) = 632\).
time = 1.23, size = 1032, normalized size = 2.89 \begin {gather*} \frac {4 \, {\left (8 \, b^{4} d^{4} x^{4} + 32 \, b^{4} c d^{3} x^{3} + 48 \, b^{4} c^{2} d^{2} x^{2} + 32 \, b^{4} c^{3} d x + 8 \, b^{4} c^{4} - 3 \, b^{4}\right )} \arcsin \left (d x + c\right )^{4} e^{3} + 16 \, {\left (8 \, a b^{3} d^{4} x^{4} + 32 \, a b^{3} c d^{3} x^{3} + 48 \, a b^{3} c^{2} d^{2} x^{2} + 32 \, a b^{3} c^{3} d x + 8 \, a b^{3} c^{4} - 3 \, a b^{3}\right )} \arcsin \left (d x + c\right )^{3} e^{3} + 3 \, {\left (8 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} d^{4} x^{4} + 32 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} c d^{3} x^{3} - 24 \, b^{4} c^{2} + 8 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} c^{4} - 24 \, {\left (b^{4} - 2 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} c^{2}\right )} d^{2} x^{2} - 24 \, a^{2} b^{2} + 15 \, b^{4} - 16 \, {\left (3 \, b^{4} c - 2 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} c^{3}\right )} d x\right )} \arcsin \left (d x + c\right )^{2} e^{3} + 2 \, {\left (8 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} d^{4} x^{4} + 32 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} c d^{3} x^{3} - 72 \, a b^{3} c^{2} + 8 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} c^{4} - 24 \, {\left (3 \, a b^{3} - 2 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} c^{2}\right )} d^{2} x^{2} - 24 \, a^{3} b + 45 \, a b^{3} - 16 \, {\left (9 \, a b^{3} c - 2 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} c^{3}\right )} d x\right )} \arcsin \left (d x + c\right ) e^{3} + {\left ({\left (32 \, a^{4} - 24 \, a^{2} b^{2} + 3 \, b^{4}\right )} d^{4} x^{4} + 4 \, {\left (32 \, a^{4} - 24 \, a^{2} b^{2} + 3 \, b^{4}\right )} c d^{3} x^{3} - 3 \, {\left (24 \, a^{2} b^{2} - 15 \, b^{4} - 2 \, {\left (32 \, a^{4} - 24 \, a^{2} b^{2} + 3 \, b^{4}\right )} c^{2}\right )} d^{2} x^{2} + 2 \, {\left (2 \, {\left (32 \, a^{4} - 24 \, a^{2} b^{2} + 3 \, b^{4}\right )} c^{3} - 9 \, {\left (8 \, a^{2} b^{2} - 5 \, b^{4}\right )} c\right )} d x\right )} e^{3} + 2 \, {\left (8 \, {\left (2 \, b^{4} d^{3} x^{3} + 6 \, b^{4} c d^{2} x^{2} + 2 \, b^{4} c^{3} + 3 \, b^{4} c + 3 \, {\left (2 \, b^{4} c^{2} + b^{4}\right )} d x\right )} \arcsin \left (d x + c\right )^{3} e^{3} + 24 \, {\left (2 \, a b^{3} d^{3} x^{3} + 6 \, a b^{3} c d^{2} x^{2} + 2 \, a b^{3} c^{3} + 3 \, a b^{3} c + 3 \, {\left (2 \, a b^{3} c^{2} + a b^{3}\right )} d x\right )} \arcsin \left (d x + c\right )^{2} e^{3} + 3 \, {\left (2 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} d^{3} x^{3} + 6 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} c d^{2} x^{2} + 2 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} c^{3} + 3 \, {\left (8 \, a^{2} b^{2} - 5 \, b^{4} + 2 \, {\left (8 \, a^{2} b^{2} - b^{4}\right )} c^{2}\right )} d x + 3 \, {\left (8 \, a^{2} b^{2} - 5 \, b^{4}\right )} c\right )} \arcsin \left (d x + c\right ) e^{3} + {\left (2 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} d^{3} x^{3} + 6 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} c d^{2} x^{2} + 2 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} c^{3} + 3 \, {\left (8 \, a^{3} b - 15 \, a b^{3} + 2 \, {\left (8 \, a^{3} b - 3 \, a b^{3}\right )} c^{2}\right )} d x + 3 \, {\left (8 \, a^{3} b - 15 \, a b^{3}\right )} c\right )} e^{3}\right )} \sqrt {-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}{128 \, d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 2876 vs.
\(2 (325) = 650\).
time = 1.54, size = 2876, normalized size = 8.06 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1016 vs.
\(2 (327) = 654\).
time = 0.48, size = 1016, normalized size = 2.85 \begin {gather*} \frac {{\left ({\left (d x + c\right )}^{2} - 1\right )}^{2} b^{4} e^{3} \arcsin \left (d x + c\right )^{4}}{4 \, d} - \frac {{\left (-{\left (d x + c\right )}^{2} + 1\right )}^{\frac {3}{2}} {\left (d x + c\right )} b^{4} e^{3} \arcsin \left (d x + c\right )^{3}}{4 \, d} + \frac {{\left ({\left (d x + c\right )}^{2} - 1\right )}^{2} a b^{3} e^{3} \arcsin \left (d x + c\right )^{3}}{d} + \frac {{\left ({\left (d x + c\right )}^{2} - 1\right )} b^{4} e^{3} \arcsin \left (d x + c\right )^{4}}{2 \, d} - \frac {3 \, {\left (-{\left (d x + c\right )}^{2} + 1\right )}^{\frac {3}{2}} {\left (d x + c\right )} a b^{3} e^{3} \arcsin \left (d x + c\right )^{2}}{4 \, d} + \frac {5 \, \sqrt {-{\left (d x + c\right )}^{2} + 1} {\left (d x + c\right )} b^{4} e^{3} \arcsin \left (d x + c\right )^{3}}{8 \, d} + \frac {{\left (d x + c\right )}^{4} a^{4} e^{3}}{4 \, d} + \frac {3 \, {\left ({\left (d x + c\right )}^{2} - 1\right )}^{2} a^{2} b^{2} e^{3} \arcsin \left (d x + c\right )^{2}}{2 \, d} - \frac {3 \, {\left ({\left (d x + c\right )}^{2} - 1\right )}^{2} b^{4} e^{3} \arcsin \left (d x + c\right )^{2}}{16 \, d} + \frac {2 \, {\left ({\left (d x + c\right )}^{2} - 1\right )} a b^{3} e^{3} \arcsin \left (d x + c\right )^{3}}{d} + \frac {5 \, b^{4} e^{3} \arcsin \left (d x + c\right )^{4}}{32 \, d} - \frac {3 \, {\left (-{\left (d x + c\right )}^{2} + 1\right )}^{\frac {3}{2}} {\left (d x + c\right )} a^{2} b^{2} e^{3} \arcsin \left (d x + c\right )}{4 \, d} + \frac {3 \, {\left (-{\left (d x + c\right )}^{2} + 1\right )}^{\frac {3}{2}} {\left (d x + c\right )} b^{4} e^{3} \arcsin \left (d x + c\right )}{32 \, d} + \frac {15 \, \sqrt {-{\left (d x + c\right )}^{2} + 1} {\left (d x + c\right )} a b^{3} e^{3} \arcsin \left (d x + c\right )^{2}}{8 \, d} + \frac {{\left ({\left (d x + c\right )}^{2} - 1\right )}^{2} a^{3} b e^{3} \arcsin \left (d x + c\right )}{d} - \frac {3 \, {\left ({\left (d x + c\right )}^{2} - 1\right )}^{2} a b^{3} e^{3} \arcsin \left (d x + c\right )}{8 \, d} + \frac {3 \, {\left ({\left (d x + c\right )}^{2} - 1\right )} a^{2} b^{2} e^{3} \arcsin \left (d x + c\right )^{2}}{d} - \frac {15 \, {\left ({\left (d x + c\right )}^{2} - 1\right )} b^{4} e^{3} \arcsin \left (d x + c\right )^{2}}{16 \, d} + \frac {5 \, a b^{3} e^{3} \arcsin \left (d x + c\right )^{3}}{8 \, d} - \frac {{\left (-{\left (d x + c\right )}^{2} + 1\right )}^{\frac {3}{2}} {\left (d x + c\right )} a^{3} b e^{3}}{4 \, d} + \frac {3 \, {\left (-{\left (d x + c\right )}^{2} + 1\right )}^{\frac {3}{2}} {\left (d x + c\right )} a b^{3} e^{3}}{32 \, d} + \frac {15 \, \sqrt {-{\left (d x + c\right )}^{2} + 1} {\left (d x + c\right )} a^{2} b^{2} e^{3} \arcsin \left (d x + c\right )}{8 \, d} - \frac {51 \, \sqrt {-{\left (d x + c\right )}^{2} + 1} {\left (d x + c\right )} b^{4} e^{3} \arcsin \left (d x + c\right )}{64 \, d} - \frac {3 \, {\left ({\left (d x + c\right )}^{2} - 1\right )}^{2} a^{2} b^{2} e^{3}}{16 \, d} + \frac {3 \, {\left ({\left (d x + c\right )}^{2} - 1\right )}^{2} b^{4} e^{3}}{128 \, d} + \frac {2 \, {\left ({\left (d x + c\right )}^{2} - 1\right )} a^{3} b e^{3} \arcsin \left (d x + c\right )}{d} - \frac {15 \, {\left ({\left (d x + c\right )}^{2} - 1\right )} a b^{3} e^{3} \arcsin \left (d x + c\right )}{8 \, d} + \frac {15 \, a^{2} b^{2} e^{3} \arcsin \left (d x + c\right )^{2}}{16 \, d} - \frac {51 \, b^{4} e^{3} \arcsin \left (d x + c\right )^{2}}{128 \, d} + \frac {5 \, \sqrt {-{\left (d x + c\right )}^{2} + 1} {\left (d x + c\right )} a^{3} b e^{3}}{8 \, d} - \frac {51 \, \sqrt {-{\left (d x + c\right )}^{2} + 1} {\left (d x + c\right )} a b^{3} e^{3}}{64 \, d} - \frac {15 \, {\left ({\left (d x + c\right )}^{2} - 1\right )} a^{2} b^{2} e^{3}}{16 \, d} + \frac {51 \, {\left ({\left (d x + c\right )}^{2} - 1\right )} b^{4} e^{3}}{128 \, d} + \frac {5 \, a^{3} b e^{3} \arcsin \left (d x + c\right )}{8 \, d} - \frac {51 \, a b^{3} e^{3} \arcsin \left (d x + c\right )}{64 \, d} - \frac {51 \, a^{2} b^{2} e^{3}}{128 \, d} + \frac {195 \, b^{4} e^{3}}{1024 \, d} \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 )}^4 \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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