Optimal. Leaf size=403 \[ \frac {3 i b c^2 \text {Li}_2\left (-e^{2 i \sin ^{-1}(c x)}\right ) \left (a+b \sin ^{-1}(c x)\right )}{d^3}-\frac {3 i b c^2 \text {Li}_2\left (e^{2 i \sin ^{-1}(c x)}\right ) \left (a+b \sin ^{-1}(c x)\right )}{d^3}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}-\frac {6 c^2 \tanh ^{-1}\left (e^{2 i \sin ^{-1}(c x)}\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{d^3}-\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {3 b^2 c^2 \text {Li}_3\left (-e^{2 i \sin ^{-1}(c x)}\right )}{2 d^3}+\frac {3 b^2 c^2 \text {Li}_3\left (e^{2 i \sin ^{-1}(c x)}\right )}{2 d^3}+\frac {b^2 c^2}{12 d^3 \left (1-c^2 x^2\right )}-\frac {7 b^2 c^2 \log \left (1-c^2 x^2\right )}{6 d^3}+\frac {b^2 c^2 \log (x)}{d^3} \]
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Rubi [A] time = 0.78, antiderivative size = 403, normalized size of antiderivative = 1.00, number of steps used = 23, number of rules used = 19, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.704, Rules used = {4701, 4705, 4679, 4419, 4183, 2531, 2282, 6589, 4651, 260, 4655, 261, 271, 192, 191, 4689, 12, 1251, 893} \[ \frac {3 i b c^2 \text {PolyLog}\left (2,-e^{2 i \sin ^{-1}(c x)}\right ) \left (a+b \sin ^{-1}(c x)\right )}{d^3}-\frac {3 i b c^2 \text {PolyLog}\left (2,e^{2 i \sin ^{-1}(c x)}\right ) \left (a+b \sin ^{-1}(c x)\right )}{d^3}-\frac {3 b^2 c^2 \text {PolyLog}\left (3,-e^{2 i \sin ^{-1}(c x)}\right )}{2 d^3}+\frac {3 b^2 c^2 \text {PolyLog}\left (3,e^{2 i \sin ^{-1}(c x)}\right )}{2 d^3}-\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}-\frac {6 c^2 \tanh ^{-1}\left (e^{2 i \sin ^{-1}(c x)}\right ) \left (a+b \sin ^{-1}(c x)\right )^2}{d^3}+\frac {b^2 c^2}{12 d^3 \left (1-c^2 x^2\right )}-\frac {7 b^2 c^2 \log \left (1-c^2 x^2\right )}{6 d^3}+\frac {b^2 c^2 \log (x)}{d^3} \]
Antiderivative was successfully verified.
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Rule 12
Rule 191
Rule 192
Rule 260
Rule 261
Rule 271
Rule 893
Rule 1251
Rule 2282
Rule 2531
Rule 4183
Rule 4419
Rule 4651
Rule 4655
Rule 4679
Rule 4689
Rule 4701
Rule 4705
Rule 6589
Rubi steps
\begin {align*} \int \frac {\left (a+b \sin ^{-1}(c x)\right )^2}{x^3 \left (d-c^2 d x^2\right )^3} \, dx &=-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}+\left (3 c^2\right ) \int \frac {\left (a+b \sin ^{-1}(c x)\right )^2}{x \left (d-c^2 d x^2\right )^3} \, dx+\frac {(b c) \int \frac {a+b \sin ^{-1}(c x)}{x^2 \left (1-c^2 x^2\right )^{5/2}} \, dx}{d^3}\\ &=-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}+\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \left (1-c^2 x^2\right )^{3/2}}+\frac {8 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}-\frac {\left (b^2 c^2\right ) \int \frac {-3+12 c^2 x^2-8 c^4 x^4}{3 x \left (1-c^2 x^2\right )^2} \, dx}{d^3}-\frac {\left (3 b c^3\right ) \int \frac {a+b \sin ^{-1}(c x)}{\left (1-c^2 x^2\right )^{5/2}} \, dx}{2 d^3}+\frac {\left (3 c^2\right ) \int \frac {\left (a+b \sin ^{-1}(c x)\right )^2}{x \left (d-c^2 d x^2\right )^2} \, dx}{d}\\ &=-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}+\frac {8 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}-\frac {\left (b^2 c^2\right ) \int \frac {-3+12 c^2 x^2-8 c^4 x^4}{x \left (1-c^2 x^2\right )^2} \, dx}{3 d^3}-\frac {\left (b c^3\right ) \int \frac {a+b \sin ^{-1}(c x)}{\left (1-c^2 x^2\right )^{3/2}} \, dx}{d^3}-\frac {\left (3 b c^3\right ) \int \frac {a+b \sin ^{-1}(c x)}{\left (1-c^2 x^2\right )^{3/2}} \, dx}{d^3}+\frac {\left (b^2 c^4\right ) \int \frac {x}{\left (1-c^2 x^2\right )^2} \, dx}{2 d^3}+\frac {\left (3 c^2\right ) \int \frac {\left (a+b \sin ^{-1}(c x)\right )^2}{x \left (d-c^2 d x^2\right )} \, dx}{d^2}\\ &=\frac {b^2 c^2}{4 d^3 \left (1-c^2 x^2\right )}-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}+\frac {\left (3 c^2\right ) \operatorname {Subst}\left (\int (a+b x)^2 \csc (x) \sec (x) \, dx,x,\sin ^{-1}(c x)\right )}{d^3}-\frac {\left (b^2 c^2\right ) \operatorname {Subst}\left (\int \frac {-3+12 c^2 x-8 c^4 x^2}{x \left (1-c^2 x\right )^2} \, dx,x,x^2\right )}{6 d^3}+\frac {\left (b^2 c^4\right ) \int \frac {x}{1-c^2 x^2} \, dx}{d^3}+\frac {\left (3 b^2 c^4\right ) \int \frac {x}{1-c^2 x^2} \, dx}{d^3}\\ &=\frac {b^2 c^2}{4 d^3 \left (1-c^2 x^2\right )}-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}-\frac {2 b^2 c^2 \log \left (1-c^2 x^2\right )}{d^3}+\frac {\left (6 c^2\right ) \operatorname {Subst}\left (\int (a+b x)^2 \csc (2 x) \, dx,x,\sin ^{-1}(c x)\right )}{d^3}-\frac {\left (b^2 c^2\right ) \operatorname {Subst}\left (\int \left (-\frac {3}{x}+\frac {c^2}{\left (-1+c^2 x\right )^2}-\frac {5 c^2}{-1+c^2 x}\right ) \, dx,x,x^2\right )}{6 d^3}\\ &=\frac {b^2 c^2}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}-\frac {6 c^2 \left (a+b \sin ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 i \sin ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1-c^2 x^2\right )}{6 d^3}-\frac {\left (6 b c^2\right ) \operatorname {Subst}\left (\int (a+b x) \log \left (1-e^{2 i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{d^3}+\frac {\left (6 b c^2\right ) \operatorname {Subst}\left (\int (a+b x) \log \left (1+e^{2 i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{d^3}\\ &=\frac {b^2 c^2}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}-\frac {6 c^2 \left (a+b \sin ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 i \sin ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1-c^2 x^2\right )}{6 d^3}+\frac {3 i b c^2 \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (-e^{2 i \sin ^{-1}(c x)}\right )}{d^3}-\frac {3 i b c^2 \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (e^{2 i \sin ^{-1}(c x)}\right )}{d^3}-\frac {\left (3 i b^2 c^2\right ) \operatorname {Subst}\left (\int \text {Li}_2\left (-e^{2 i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{d^3}+\frac {\left (3 i b^2 c^2\right ) \operatorname {Subst}\left (\int \text {Li}_2\left (e^{2 i x}\right ) \, dx,x,\sin ^{-1}(c x)\right )}{d^3}\\ &=\frac {b^2 c^2}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}-\frac {6 c^2 \left (a+b \sin ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 i \sin ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1-c^2 x^2\right )}{6 d^3}+\frac {3 i b c^2 \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (-e^{2 i \sin ^{-1}(c x)}\right )}{d^3}-\frac {3 i b c^2 \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (e^{2 i \sin ^{-1}(c x)}\right )}{d^3}-\frac {\left (3 b^2 c^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2(-x)}{x} \, dx,x,e^{2 i \sin ^{-1}(c x)}\right )}{2 d^3}+\frac {\left (3 b^2 c^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2(x)}{x} \, dx,x,e^{2 i \sin ^{-1}(c x)}\right )}{2 d^3}\\ &=\frac {b^2 c^2}{12 d^3 \left (1-c^2 x^2\right )}-\frac {b c \left (a+b \sin ^{-1}(c x)\right )}{d^3 x \left (1-c^2 x^2\right )^{3/2}}+\frac {5 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{6 d^3 \left (1-c^2 x^2\right )^{3/2}}-\frac {4 b c^3 x \left (a+b \sin ^{-1}(c x)\right )}{3 d^3 \sqrt {1-c^2 x^2}}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{4 d^3 \left (1-c^2 x^2\right )^2}-\frac {\left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 x^2 \left (1-c^2 x^2\right )^2}+\frac {3 c^2 \left (a+b \sin ^{-1}(c x)\right )^2}{2 d^3 \left (1-c^2 x^2\right )}-\frac {6 c^2 \left (a+b \sin ^{-1}(c x)\right )^2 \tanh ^{-1}\left (e^{2 i \sin ^{-1}(c x)}\right )}{d^3}+\frac {b^2 c^2 \log (x)}{d^3}-\frac {7 b^2 c^2 \log \left (1-c^2 x^2\right )}{6 d^3}+\frac {3 i b c^2 \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (-e^{2 i \sin ^{-1}(c x)}\right )}{d^3}-\frac {3 i b c^2 \left (a+b \sin ^{-1}(c x)\right ) \text {Li}_2\left (e^{2 i \sin ^{-1}(c x)}\right )}{d^3}-\frac {3 b^2 c^2 \text {Li}_3\left (-e^{2 i \sin ^{-1}(c x)}\right )}{2 d^3}+\frac {3 b^2 c^2 \text {Li}_3\left (e^{2 i \sin ^{-1}(c x)}\right )}{2 d^3}\\ \end {align*}
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Mathematica [A] time = 7.91, size = 569, normalized size = 1.41 \[ -\frac {\frac {12 a^2 c^2}{c^2 x^2-1}-\frac {3 a^2 c^2}{\left (c^2 x^2-1\right )^2}+18 a^2 c^2 \log \left (1-c^2 x^2\right )-36 a^2 c^2 \log (x)+\frac {6 a^2}{x^2}+2 a b c^2 \left (\frac {14 c x}{\sqrt {1-c^2 x^2}}+\frac {c x}{\left (1-c^2 x^2\right )^{3/2}}+\frac {6 \sqrt {1-c^2 x^2}}{c x}+\frac {12 \sin ^{-1}(c x)}{c^2 x^2-1}-\frac {3 \sin ^{-1}(c x)}{\left (c^2 x^2-1\right )^2}+\frac {6 \sin ^{-1}(c x)}{c^2 x^2}-18 i \text {Li}_2\left (-e^{2 i \sin ^{-1}(c x)}\right )+18 i \text {Li}_2\left (e^{2 i \sin ^{-1}(c x)}\right )-36 \sin ^{-1}(c x) \log \left (1-e^{2 i \sin ^{-1}(c x)}\right )+36 \sin ^{-1}(c x) \log \left (1+e^{2 i \sin ^{-1}(c x)}\right )\right )+12 b^2 c^2 \left (\frac {1}{24} \left (\frac {2}{c^2 x^2-1}+28 \log \left (1-c^2 x^2\right )+\frac {24 \sin ^{-1}(c x)^2}{c^2 x^2-1}+\frac {12 \sin ^{-1}(c x)^2}{c^2 x^2}-\frac {6 \sin ^{-1}(c x)^2}{\left (c^2 x^2-1\right )^2}+\frac {24 \sqrt {1-c^2 x^2} \sin ^{-1}(c x)}{c x}+\frac {56 c x \sin ^{-1}(c x)}{\sqrt {1-c^2 x^2}}+\frac {4 c x \sin ^{-1}(c x)}{\left (1-c^2 x^2\right )^{3/2}}-36 \text {Li}_3\left (e^{-2 i \sin ^{-1}(c x)}\right )+36 \text {Li}_3\left (-e^{2 i \sin ^{-1}(c x)}\right )-24 \log (c x)-48 i \sin ^{-1}(c x)^3-72 \sin ^{-1}(c x)^2 \log \left (1-e^{-2 i \sin ^{-1}(c x)}\right )+72 \sin ^{-1}(c x)^2 \log \left (1+e^{2 i \sin ^{-1}(c x)}\right )+3 i \pi ^3\right )-3 i \sin ^{-1}(c x) \text {Li}_2\left (e^{-2 i \sin ^{-1}(c x)}\right )-3 i \sin ^{-1}(c x) \text {Li}_2\left (-e^{2 i \sin ^{-1}(c x)}\right )\right )}{12 d^3} \]
Warning: Unable to verify antiderivative.
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fricas [F] time = 0.58, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {b^{2} \arcsin \left (c x\right )^{2} + 2 \, a b \arcsin \left (c x\right ) + a^{2}}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int -\frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2}}{{\left (c^{2} d x^{2} - d\right )}^{3} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.59, size = 1547, normalized size = 3.84 \[ \text {result too large to display} \]
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 \[ -\frac {1}{4} \, a^{2} {\left (\frac {6 \, c^{4} x^{4} - 9 \, c^{2} x^{2} + 2}{c^{4} d^{3} x^{6} - 2 \, c^{2} d^{3} x^{4} + d^{3} x^{2}} + \frac {6 \, c^{2} \log \left (c x + 1\right )}{d^{3}} + \frac {6 \, c^{2} \log \left (c x - 1\right )}{d^{3}} - \frac {12 \, c^{2} \log \relax (x)}{d^{3}}\right )} - \int \frac {b^{2} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right )^{2} + 2 \, a b \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right )}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}\,{d x} \]
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 \[ \int \frac {{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2}{x^3\,{\left (d-c^2\,d\,x^2\right )}^3} \,d x \]
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 \[ - \frac {\int \frac {a^{2}}{c^{6} x^{9} - 3 c^{4} x^{7} + 3 c^{2} x^{5} - x^{3}}\, dx + \int \frac {b^{2} \operatorname {asin}^{2}{\left (c x \right )}}{c^{6} x^{9} - 3 c^{4} x^{7} + 3 c^{2} x^{5} - x^{3}}\, dx + \int \frac {2 a b \operatorname {asin}{\left (c x \right )}}{c^{6} x^{9} - 3 c^{4} x^{7} + 3 c^{2} x^{5} - x^{3}}\, dx}{d^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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