Optimal. Leaf size=302 \[ -\frac {73 b^2 d^2 x^2}{3072 c^2}-\frac {73 b^2 d^2 x^4}{9216}+\frac {43 b^2 c^2 d^2 x^6}{3456}-\frac {1}{256} b^2 c^4 d^2 x^8+\frac {73 b d^2 x \sqrt {1-c^2 x^2} (a+b \text {ArcSin}(c x))}{1536 c^3}+\frac {73 b d^2 x^3 \sqrt {1-c^2 x^2} (a+b \text {ArcSin}(c x))}{2304 c}-\frac {25}{576} b c d^2 x^5 \sqrt {1-c^2 x^2} (a+b \text {ArcSin}(c x))-\frac {1}{32} b c d^2 x^5 \left (1-c^2 x^2\right )^{3/2} (a+b \text {ArcSin}(c x))-\frac {73 d^2 (a+b \text {ArcSin}(c x))^2}{3072 c^4}+\frac {1}{24} d^2 x^4 (a+b \text {ArcSin}(c x))^2+\frac {1}{12} d^2 x^4 \left (1-c^2 x^2\right ) (a+b \text {ArcSin}(c x))^2+\frac {1}{8} d^2 x^4 \left (1-c^2 x^2\right )^2 (a+b \text {ArcSin}(c x))^2 \]
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Rubi [A]
time = 0.69, antiderivative size = 302, normalized size of antiderivative = 1.00, number of steps
used = 25, number of rules used = 7, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.259, Rules used = {4787, 4723,
4795, 4737, 30, 4783, 14} \begin {gather*} -\frac {73 d^2 (a+b \text {ArcSin}(c x))^2}{3072 c^4}-\frac {1}{32} b c d^2 x^5 \left (1-c^2 x^2\right )^{3/2} (a+b \text {ArcSin}(c x))-\frac {25}{576} b c d^2 x^5 \sqrt {1-c^2 x^2} (a+b \text {ArcSin}(c x))+\frac {1}{8} d^2 x^4 \left (1-c^2 x^2\right )^2 (a+b \text {ArcSin}(c x))^2+\frac {1}{12} d^2 x^4 \left (1-c^2 x^2\right ) (a+b \text {ArcSin}(c x))^2+\frac {73 b d^2 x^3 \sqrt {1-c^2 x^2} (a+b \text {ArcSin}(c x))}{2304 c}+\frac {73 b d^2 x \sqrt {1-c^2 x^2} (a+b \text {ArcSin}(c x))}{1536 c^3}+\frac {1}{24} d^2 x^4 (a+b \text {ArcSin}(c x))^2-\frac {1}{256} b^2 c^4 d^2 x^8+\frac {43 b^2 c^2 d^2 x^6}{3456}-\frac {73 b^2 d^2 x^2}{3072 c^2}-\frac {73 b^2 d^2 x^4}{9216} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 30
Rule 4723
Rule 4737
Rule 4783
Rule 4787
Rule 4795
Rubi steps
\begin {align*} \int x^3 \left (d-c^2 d x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2 \, dx &=\frac {1}{8} d^2 x^4 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{2} d \int x^3 \left (d-c^2 d x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2 \, dx-\frac {1}{4} \left (b c d^2\right ) \int x^4 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right ) \, dx\\ &=-\frac {1}{32} b c d^2 x^5 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )+\frac {1}{12} d^2 x^4 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{8} d^2 x^4 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{6} d^2 \int x^3 \left (a+b \sin ^{-1}(c x)\right )^2 \, dx-\frac {1}{32} \left (3 b c d^2\right ) \int x^4 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right ) \, dx-\frac {1}{6} \left (b c d^2\right ) \int x^4 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right ) \, dx+\frac {1}{32} \left (b^2 c^2 d^2\right ) \int x^5 \left (1-c^2 x^2\right ) \, dx\\ &=-\frac {25}{576} b c d^2 x^5 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{32} b c d^2 x^5 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )+\frac {1}{24} d^2 x^4 \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{12} d^2 x^4 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{8} d^2 x^4 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2-\frac {1}{64} \left (b c d^2\right ) \int \frac {x^4 \left (a+b \sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}} \, dx-\frac {1}{36} \left (b c d^2\right ) \int \frac {x^4 \left (a+b \sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}} \, dx-\frac {1}{12} \left (b c d^2\right ) \int \frac {x^4 \left (a+b \sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}} \, dx+\frac {1}{64} \left (b^2 c^2 d^2\right ) \int x^5 \, dx+\frac {1}{36} \left (b^2 c^2 d^2\right ) \int x^5 \, dx+\frac {1}{32} \left (b^2 c^2 d^2\right ) \int \left (x^5-c^2 x^7\right ) \, dx\\ &=\frac {43 b^2 c^2 d^2 x^6}{3456}-\frac {1}{256} b^2 c^4 d^2 x^8+\frac {73 b d^2 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2304 c}-\frac {25}{576} b c d^2 x^5 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{32} b c d^2 x^5 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )+\frac {1}{24} d^2 x^4 \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{12} d^2 x^4 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{8} d^2 x^4 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2-\frac {1}{256} \left (b^2 d^2\right ) \int x^3 \, dx-\frac {1}{144} \left (b^2 d^2\right ) \int x^3 \, dx-\frac {1}{48} \left (b^2 d^2\right ) \int x^3 \, dx-\frac {\left (3 b d^2\right ) \int \frac {x^2 \left (a+b \sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}} \, dx}{256 c}-\frac {\left (b d^2\right ) \int \frac {x^2 \left (a+b \sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}} \, dx}{48 c}-\frac {\left (b d^2\right ) \int \frac {x^2 \left (a+b \sin ^{-1}(c x)\right )}{\sqrt {1-c^2 x^2}} \, dx}{16 c}\\ &=-\frac {73 b^2 d^2 x^4}{9216}+\frac {43 b^2 c^2 d^2 x^6}{3456}-\frac {1}{256} b^2 c^4 d^2 x^8+\frac {73 b d^2 x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{1536 c^3}+\frac {73 b d^2 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2304 c}-\frac {25}{576} b c d^2 x^5 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{32} b c d^2 x^5 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )+\frac {1}{24} d^2 x^4 \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{12} d^2 x^4 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{8} d^2 x^4 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2-\frac {\left (3 b d^2\right ) \int \frac {a+b \sin ^{-1}(c x)}{\sqrt {1-c^2 x^2}} \, dx}{512 c^3}-\frac {\left (b d^2\right ) \int \frac {a+b \sin ^{-1}(c x)}{\sqrt {1-c^2 x^2}} \, dx}{96 c^3}-\frac {\left (b d^2\right ) \int \frac {a+b \sin ^{-1}(c x)}{\sqrt {1-c^2 x^2}} \, dx}{32 c^3}-\frac {\left (3 b^2 d^2\right ) \int x \, dx}{512 c^2}-\frac {\left (b^2 d^2\right ) \int x \, dx}{96 c^2}-\frac {\left (b^2 d^2\right ) \int x \, dx}{32 c^2}\\ &=-\frac {73 b^2 d^2 x^2}{3072 c^2}-\frac {73 b^2 d^2 x^4}{9216}+\frac {43 b^2 c^2 d^2 x^6}{3456}-\frac {1}{256} b^2 c^4 d^2 x^8+\frac {73 b d^2 x \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{1536 c^3}+\frac {73 b d^2 x^3 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )}{2304 c}-\frac {25}{576} b c d^2 x^5 \sqrt {1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )-\frac {1}{32} b c d^2 x^5 \left (1-c^2 x^2\right )^{3/2} \left (a+b \sin ^{-1}(c x)\right )-\frac {73 d^2 \left (a+b \sin ^{-1}(c x)\right )^2}{3072 c^4}+\frac {1}{24} d^2 x^4 \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{12} d^2 x^4 \left (1-c^2 x^2\right ) \left (a+b \sin ^{-1}(c x)\right )^2+\frac {1}{8} d^2 x^4 \left (1-c^2 x^2\right )^2 \left (a+b \sin ^{-1}(c x)\right )^2\\ \end {align*}
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Mathematica [A]
time = 0.15, size = 239, normalized size = 0.79 \begin {gather*} \frac {d^2 \left (c x \left (1152 a^2 c^3 x^3 \left (6-8 c^2 x^2+3 c^4 x^4\right )-b^2 c x \left (657+219 c^2 x^2-344 c^4 x^4+108 c^6 x^6\right )+6 a b \sqrt {1-c^2 x^2} \left (219+146 c^2 x^2-344 c^4 x^4+144 c^6 x^6\right )\right )+6 b \left (b c x \sqrt {1-c^2 x^2} \left (219+146 c^2 x^2-344 c^4 x^4+144 c^6 x^6\right )+3 a \left (-73+768 c^4 x^4-1024 c^6 x^6+384 c^8 x^8\right )\right ) \text {ArcSin}(c x)+9 b^2 \left (-73+768 c^4 x^4-1024 c^6 x^6+384 c^8 x^8\right ) \text {ArcSin}(c x)^2\right )}{27648 c^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 424, normalized size = 1.40
method | result | size |
derivativedivides | \(\frac {d^{2} a^{2} \left (\frac {1}{8} c^{8} x^{8}-\frac {1}{3} c^{6} x^{6}+\frac {1}{4} c^{4} x^{4}\right )+d^{2} b^{2} \left (\frac {\arcsin \left (c x \right )^{2} \left (c^{2} x^{2}-1\right )^{3}}{6}+\frac {\arcsin \left (c x \right ) \left (8 c^{5} x^{5} \sqrt {-c^{2} x^{2}+1}-26 c^{3} x^{3} \sqrt {-c^{2} x^{2}+1}+33 c x \sqrt {-c^{2} x^{2}+1}+15 \arcsin \left (c x \right )\right )}{144}-\frac {55 \arcsin \left (c x \right )^{2}}{3072}-\frac {11 \left (c^{2} x^{2}-1\right )^{3}}{3456}+\frac {55 \left (c^{2} x^{2}-1\right )^{2}}{9216}-\frac {55 c^{2} x^{2}}{3072}+\frac {55}{3072}+\frac {\arcsin \left (c x \right )^{2} \left (c^{2} x^{2}-1\right )^{4}}{8}-\frac {\arcsin \left (c x \right ) \left (-48 c^{7} x^{7} \sqrt {-c^{2} x^{2}+1}+200 c^{5} x^{5} \sqrt {-c^{2} x^{2}+1}-326 c^{3} x^{3} \sqrt {-c^{2} x^{2}+1}+279 c x \sqrt {-c^{2} x^{2}+1}+105 \arcsin \left (c x \right )\right )}{1536}-\frac {\left (c^{2} x^{2}-1\right )^{4}}{256}\right )+2 d^{2} a b \left (\frac {\arcsin \left (c x \right ) c^{8} x^{8}}{8}-\frac {\arcsin \left (c x \right ) c^{6} x^{6}}{3}+\frac {c^{4} x^{4} \arcsin \left (c x \right )}{4}+\frac {c^{7} x^{7} \sqrt {-c^{2} x^{2}+1}}{64}-\frac {43 c^{5} x^{5} \sqrt {-c^{2} x^{2}+1}}{1152}+\frac {73 c^{3} x^{3} \sqrt {-c^{2} x^{2}+1}}{4608}+\frac {73 c x \sqrt {-c^{2} x^{2}+1}}{3072}-\frac {73 \arcsin \left (c x \right )}{3072}\right )}{c^{4}}\) | \(424\) |
default | \(\frac {d^{2} a^{2} \left (\frac {1}{8} c^{8} x^{8}-\frac {1}{3} c^{6} x^{6}+\frac {1}{4} c^{4} x^{4}\right )+d^{2} b^{2} \left (\frac {\arcsin \left (c x \right )^{2} \left (c^{2} x^{2}-1\right )^{3}}{6}+\frac {\arcsin \left (c x \right ) \left (8 c^{5} x^{5} \sqrt {-c^{2} x^{2}+1}-26 c^{3} x^{3} \sqrt {-c^{2} x^{2}+1}+33 c x \sqrt {-c^{2} x^{2}+1}+15 \arcsin \left (c x \right )\right )}{144}-\frac {55 \arcsin \left (c x \right )^{2}}{3072}-\frac {11 \left (c^{2} x^{2}-1\right )^{3}}{3456}+\frac {55 \left (c^{2} x^{2}-1\right )^{2}}{9216}-\frac {55 c^{2} x^{2}}{3072}+\frac {55}{3072}+\frac {\arcsin \left (c x \right )^{2} \left (c^{2} x^{2}-1\right )^{4}}{8}-\frac {\arcsin \left (c x \right ) \left (-48 c^{7} x^{7} \sqrt {-c^{2} x^{2}+1}+200 c^{5} x^{5} \sqrt {-c^{2} x^{2}+1}-326 c^{3} x^{3} \sqrt {-c^{2} x^{2}+1}+279 c x \sqrt {-c^{2} x^{2}+1}+105 \arcsin \left (c x \right )\right )}{1536}-\frac {\left (c^{2} x^{2}-1\right )^{4}}{256}\right )+2 d^{2} a b \left (\frac {\arcsin \left (c x \right ) c^{8} x^{8}}{8}-\frac {\arcsin \left (c x \right ) c^{6} x^{6}}{3}+\frac {c^{4} x^{4} \arcsin \left (c x \right )}{4}+\frac {c^{7} x^{7} \sqrt {-c^{2} x^{2}+1}}{64}-\frac {43 c^{5} x^{5} \sqrt {-c^{2} x^{2}+1}}{1152}+\frac {73 c^{3} x^{3} \sqrt {-c^{2} x^{2}+1}}{4608}+\frac {73 c x \sqrt {-c^{2} x^{2}+1}}{3072}-\frac {73 \arcsin \left (c x \right )}{3072}\right )}{c^{4}}\) | \(424\) |
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 [A]
time = 2.34, size = 319, normalized size = 1.06 \begin {gather*} \frac {108 \, {\left (32 \, a^{2} - b^{2}\right )} c^{8} d^{2} x^{8} - 8 \, {\left (1152 \, a^{2} - 43 \, b^{2}\right )} c^{6} d^{2} x^{6} + 3 \, {\left (2304 \, a^{2} - 73 \, b^{2}\right )} c^{4} d^{2} x^{4} - 657 \, b^{2} c^{2} d^{2} x^{2} + 9 \, {\left (384 \, b^{2} c^{8} d^{2} x^{8} - 1024 \, b^{2} c^{6} d^{2} x^{6} + 768 \, b^{2} c^{4} d^{2} x^{4} - 73 \, b^{2} d^{2}\right )} \arcsin \left (c x\right )^{2} + 18 \, {\left (384 \, a b c^{8} d^{2} x^{8} - 1024 \, a b c^{6} d^{2} x^{6} + 768 \, a b c^{4} d^{2} x^{4} - 73 \, a b d^{2}\right )} \arcsin \left (c x\right ) + 6 \, {\left (144 \, a b c^{7} d^{2} x^{7} - 344 \, a b c^{5} d^{2} x^{5} + 146 \, a b c^{3} d^{2} x^{3} + 219 \, a b c d^{2} x + {\left (144 \, b^{2} c^{7} d^{2} x^{7} - 344 \, b^{2} c^{5} d^{2} x^{5} + 146 \, b^{2} c^{3} d^{2} x^{3} + 219 \, b^{2} c d^{2} x\right )} \arcsin \left (c x\right )\right )} \sqrt {-c^{2} x^{2} + 1}}{27648 \, c^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.75, size = 515, normalized size = 1.71 \begin {gather*} \begin {cases} \frac {a^{2} c^{4} d^{2} x^{8}}{8} - \frac {a^{2} c^{2} d^{2} x^{6}}{3} + \frac {a^{2} d^{2} x^{4}}{4} + \frac {a b c^{4} d^{2} x^{8} \operatorname {asin}{\left (c x \right )}}{4} + \frac {a b c^{3} d^{2} x^{7} \sqrt {- c^{2} x^{2} + 1}}{32} - \frac {2 a b c^{2} d^{2} x^{6} \operatorname {asin}{\left (c x \right )}}{3} - \frac {43 a b c d^{2} x^{5} \sqrt {- c^{2} x^{2} + 1}}{576} + \frac {a b d^{2} x^{4} \operatorname {asin}{\left (c x \right )}}{2} + \frac {73 a b d^{2} x^{3} \sqrt {- c^{2} x^{2} + 1}}{2304 c} + \frac {73 a b d^{2} x \sqrt {- c^{2} x^{2} + 1}}{1536 c^{3}} - \frac {73 a b d^{2} \operatorname {asin}{\left (c x \right )}}{1536 c^{4}} + \frac {b^{2} c^{4} d^{2} x^{8} \operatorname {asin}^{2}{\left (c x \right )}}{8} - \frac {b^{2} c^{4} d^{2} x^{8}}{256} + \frac {b^{2} c^{3} d^{2} x^{7} \sqrt {- c^{2} x^{2} + 1} \operatorname {asin}{\left (c x \right )}}{32} - \frac {b^{2} c^{2} d^{2} x^{6} \operatorname {asin}^{2}{\left (c x \right )}}{3} + \frac {43 b^{2} c^{2} d^{2} x^{6}}{3456} - \frac {43 b^{2} c d^{2} x^{5} \sqrt {- c^{2} x^{2} + 1} \operatorname {asin}{\left (c x \right )}}{576} + \frac {b^{2} d^{2} x^{4} \operatorname {asin}^{2}{\left (c x \right )}}{4} - \frac {73 b^{2} d^{2} x^{4}}{9216} + \frac {73 b^{2} d^{2} x^{3} \sqrt {- c^{2} x^{2} + 1} \operatorname {asin}{\left (c x \right )}}{2304 c} - \frac {73 b^{2} d^{2} x^{2}}{3072 c^{2}} + \frac {73 b^{2} d^{2} x \sqrt {- c^{2} x^{2} + 1} \operatorname {asin}{\left (c x \right )}}{1536 c^{3}} - \frac {73 b^{2} d^{2} \operatorname {asin}^{2}{\left (c x \right )}}{3072 c^{4}} & \text {for}\: c \neq 0 \\\frac {a^{2} d^{2} x^{4}}{4} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 522, normalized size = 1.73 \begin {gather*} \frac {1}{8} \, a^{2} c^{4} d^{2} x^{8} - \frac {1}{3} \, a^{2} c^{2} d^{2} x^{6} + \frac {1}{4} \, a^{2} d^{2} x^{4} + \frac {{\left (c^{2} x^{2} - 1\right )}^{3} \sqrt {-c^{2} x^{2} + 1} b^{2} d^{2} x \arcsin \left (c x\right )}{32 \, c^{3}} + \frac {{\left (c^{2} x^{2} - 1\right )}^{4} b^{2} d^{2} \arcsin \left (c x\right )^{2}}{8 \, c^{4}} + \frac {{\left (c^{2} x^{2} - 1\right )}^{3} \sqrt {-c^{2} x^{2} + 1} a b d^{2} x}{32 \, c^{3}} + \frac {11 \, {\left (c^{2} x^{2} - 1\right )}^{2} \sqrt {-c^{2} x^{2} + 1} b^{2} d^{2} x \arcsin \left (c x\right )}{576 \, c^{3}} + \frac {{\left (c^{2} x^{2} - 1\right )}^{4} a b d^{2} \arcsin \left (c x\right )}{4 \, c^{4}} + \frac {{\left (c^{2} x^{2} - 1\right )}^{3} b^{2} d^{2} \arcsin \left (c x\right )^{2}}{6 \, c^{4}} + \frac {11 \, {\left (c^{2} x^{2} - 1\right )}^{2} \sqrt {-c^{2} x^{2} + 1} a b d^{2} x}{576 \, c^{3}} + \frac {55 \, {\left (-c^{2} x^{2} + 1\right )}^{\frac {3}{2}} b^{2} d^{2} x \arcsin \left (c x\right )}{2304 \, c^{3}} - \frac {{\left (c^{2} x^{2} - 1\right )}^{4} b^{2} d^{2}}{256 \, c^{4}} + \frac {{\left (c^{2} x^{2} - 1\right )}^{3} a b d^{2} \arcsin \left (c x\right )}{3 \, c^{4}} + \frac {55 \, {\left (-c^{2} x^{2} + 1\right )}^{\frac {3}{2}} a b d^{2} x}{2304 \, c^{3}} + \frac {55 \, \sqrt {-c^{2} x^{2} + 1} b^{2} d^{2} x \arcsin \left (c x\right )}{1536 \, c^{3}} - \frac {11 \, {\left (c^{2} x^{2} - 1\right )}^{3} b^{2} d^{2}}{3456 \, c^{4}} + \frac {55 \, \sqrt {-c^{2} x^{2} + 1} a b d^{2} x}{1536 \, c^{3}} + \frac {55 \, {\left (c^{2} x^{2} - 1\right )}^{2} b^{2} d^{2}}{9216 \, c^{4}} + \frac {55 \, b^{2} d^{2} \arcsin \left (c x\right )^{2}}{3072 \, c^{4}} - \frac {55 \, {\left (c^{2} x^{2} - 1\right )} b^{2} d^{2}}{3072 \, c^{4}} + \frac {55 \, a b d^{2} \arcsin \left (c x\right )}{1536 \, c^{4}} - \frac {9835 \, b^{2} d^{2}}{884736 \, c^{4}} \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 x^3\,{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2\,{\left (d-c^2\,d\,x^2\right )}^2 \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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