Optimal. Leaf size=317 \[ -\frac {\sqrt [4]{c} \left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}+\sqrt {a}+\sqrt {c} x\right )}{8 \sqrt {2} a^{11/4}}+\frac {\sqrt [4]{c} \left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}+\sqrt {a}+\sqrt {c} x\right )}{8 \sqrt {2} a^{11/4}}+\frac {\sqrt [4]{c} \left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4}}-\frac {\sqrt [4]{c} \left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{11/4}}-\frac {7 A}{6 a^2 x^{3/2}}-\frac {5 B}{2 a^2 \sqrt {x}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )} \]
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Rubi [A] time = 0.35, antiderivative size = 317, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 9, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.450, Rules used = {823, 829, 827, 1168, 1162, 617, 204, 1165, 628} \begin {gather*} -\frac {\sqrt [4]{c} \left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}+\sqrt {a}+\sqrt {c} x\right )}{8 \sqrt {2} a^{11/4}}+\frac {\sqrt [4]{c} \left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}+\sqrt {a}+\sqrt {c} x\right )}{8 \sqrt {2} a^{11/4}}+\frac {\sqrt [4]{c} \left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4}}-\frac {\sqrt [4]{c} \left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{11/4}}-\frac {7 A}{6 a^2 x^{3/2}}-\frac {5 B}{2 a^2 \sqrt {x}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 204
Rule 617
Rule 628
Rule 823
Rule 827
Rule 829
Rule 1162
Rule 1165
Rule 1168
Rubi steps
\begin {align*} \int \frac {A+B x}{x^{5/2} \left (a+c x^2\right )^2} \, dx &=\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )}-\frac {\int \frac {-\frac {7}{2} a A c-\frac {5}{2} a B c x}{x^{5/2} \left (a+c x^2\right )} \, dx}{2 a^2 c}\\ &=-\frac {7 A}{6 a^2 x^{3/2}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )}-\frac {\int \frac {-\frac {5}{2} a^2 B c+\frac {7}{2} a A c^2 x}{x^{3/2} \left (a+c x^2\right )} \, dx}{2 a^3 c}\\ &=-\frac {7 A}{6 a^2 x^{3/2}}-\frac {5 B}{2 a^2 \sqrt {x}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )}-\frac {\int \frac {\frac {7}{2} a^2 A c^2+\frac {5}{2} a^2 B c^2 x}{\sqrt {x} \left (a+c x^2\right )} \, dx}{2 a^4 c}\\ &=-\frac {7 A}{6 a^2 x^{3/2}}-\frac {5 B}{2 a^2 \sqrt {x}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )}-\frac {\operatorname {Subst}\left (\int \frac {\frac {7}{2} a^2 A c^2+\frac {5}{2} a^2 B c^2 x^2}{a+c x^4} \, dx,x,\sqrt {x}\right )}{a^4 c}\\ &=-\frac {7 A}{6 a^2 x^{3/2}}-\frac {5 B}{2 a^2 \sqrt {x}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )}+\frac {\left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a} \sqrt {c}-c x^2}{a+c x^4} \, dx,x,\sqrt {x}\right )}{4 a^{5/2}}-\frac {\left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a} \sqrt {c}+c x^2}{a+c x^4} \, dx,x,\sqrt {x}\right )}{4 a^{5/2}}\\ &=-\frac {7 A}{6 a^2 x^{3/2}}-\frac {5 B}{2 a^2 \sqrt {x}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )}-\frac {\left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {a}}{\sqrt {c}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{c}}+x^2} \, dx,x,\sqrt {x}\right )}{8 a^{5/2}}-\frac {\left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {a}}{\sqrt {c}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{c}}+x^2} \, dx,x,\sqrt {x}\right )}{8 a^{5/2}}-\frac {\left (\left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \sqrt [4]{c}\right ) \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{a}}{\sqrt [4]{c}}+2 x}{-\frac {\sqrt {a}}{\sqrt {c}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{c}}-x^2} \, dx,x,\sqrt {x}\right )}{8 \sqrt {2} a^{11/4}}-\frac {\left (\left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \sqrt [4]{c}\right ) \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{a}}{\sqrt [4]{c}}-2 x}{-\frac {\sqrt {a}}{\sqrt {c}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{c}}-x^2} \, dx,x,\sqrt {x}\right )}{8 \sqrt {2} a^{11/4}}\\ &=-\frac {7 A}{6 a^2 x^{3/2}}-\frac {5 B}{2 a^2 \sqrt {x}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )}-\frac {\left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \sqrt [4]{c} \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}+\sqrt {c} x\right )}{8 \sqrt {2} a^{11/4}}+\frac {\left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \sqrt [4]{c} \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}+\sqrt {c} x\right )}{8 \sqrt {2} a^{11/4}}-\frac {\left (\left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \sqrt [4]{c}\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4}}+\frac {\left (\left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \sqrt [4]{c}\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4}}\\ &=-\frac {7 A}{6 a^2 x^{3/2}}-\frac {5 B}{2 a^2 \sqrt {x}}+\frac {A+B x}{2 a x^{3/2} \left (a+c x^2\right )}+\frac {\left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \sqrt [4]{c} \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4}}-\frac {\left (5 \sqrt {a} B+7 A \sqrt {c}\right ) \sqrt [4]{c} \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{c} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{11/4}}-\frac {\left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \sqrt [4]{c} \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}+\sqrt {c} x\right )}{8 \sqrt {2} a^{11/4}}+\frac {\left (5 \sqrt {a} B-7 A \sqrt {c}\right ) \sqrt [4]{c} \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}+\sqrt {c} x\right )}{8 \sqrt {2} a^{11/4}}\\ \end {align*}
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Mathematica [C] time = 0.03, size = 85, normalized size = 0.27 \begin {gather*} \frac {3 a (A+B x)-7 A \left (a+c x^2\right ) \, _2F_1\left (-\frac {3}{4},1;\frac {1}{4};-\frac {c x^2}{a}\right )-15 B x \left (a+c x^2\right ) \, _2F_1\left (-\frac {1}{4},1;\frac {3}{4};-\frac {c x^2}{a}\right )}{6 a^2 x^{3/2} \left (a+c x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.86, size = 191, normalized size = 0.60 \begin {gather*} \frac {\left (5 \sqrt {a} B \sqrt [4]{c}+7 A c^{3/4}\right ) \tan ^{-1}\left (\frac {\sqrt {a}-\sqrt {c} x}{\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}}\right )}{4 \sqrt {2} a^{11/4}}+\frac {\left (5 \sqrt {a} B \sqrt [4]{c}-7 A c^{3/4}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a} \sqrt [4]{c} \sqrt {x}}{\sqrt {a}+\sqrt {c} x}\right )}{4 \sqrt {2} a^{11/4}}+\frac {-4 a A-12 a B x-7 A c x^2-15 B c x^3}{6 a^2 x^{3/2} \left (a+c x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.45, size = 916, normalized size = 2.89 \begin {gather*} -\frac {3 \, {\left (a^{2} c x^{4} + a^{3} x^{2}\right )} \sqrt {-\frac {a^{5} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 70 \, A B c}{a^{5}}} \log \left (-{\left (625 \, B^{4} a^{2} c - 2401 \, A^{4} c^{3}\right )} \sqrt {x} + {\left (5 \, B a^{9} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 175 \, A B^{2} a^{4} c + 343 \, A^{3} a^{3} c^{2}\right )} \sqrt {-\frac {a^{5} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 70 \, A B c}{a^{5}}}\right ) - 3 \, {\left (a^{2} c x^{4} + a^{3} x^{2}\right )} \sqrt {-\frac {a^{5} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 70 \, A B c}{a^{5}}} \log \left (-{\left (625 \, B^{4} a^{2} c - 2401 \, A^{4} c^{3}\right )} \sqrt {x} - {\left (5 \, B a^{9} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 175 \, A B^{2} a^{4} c + 343 \, A^{3} a^{3} c^{2}\right )} \sqrt {-\frac {a^{5} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 70 \, A B c}{a^{5}}}\right ) - 3 \, {\left (a^{2} c x^{4} + a^{3} x^{2}\right )} \sqrt {\frac {a^{5} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 70 \, A B c}{a^{5}}} \log \left (-{\left (625 \, B^{4} a^{2} c - 2401 \, A^{4} c^{3}\right )} \sqrt {x} + {\left (5 \, B a^{9} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 175 \, A B^{2} a^{4} c - 343 \, A^{3} a^{3} c^{2}\right )} \sqrt {\frac {a^{5} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 70 \, A B c}{a^{5}}}\right ) + 3 \, {\left (a^{2} c x^{4} + a^{3} x^{2}\right )} \sqrt {\frac {a^{5} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 70 \, A B c}{a^{5}}} \log \left (-{\left (625 \, B^{4} a^{2} c - 2401 \, A^{4} c^{3}\right )} \sqrt {x} - {\left (5 \, B a^{9} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} + 175 \, A B^{2} a^{4} c - 343 \, A^{3} a^{3} c^{2}\right )} \sqrt {\frac {a^{5} \sqrt {-\frac {625 \, B^{4} a^{2} c - 2450 \, A^{2} B^{2} a c^{2} + 2401 \, A^{4} c^{3}}{a^{11}}} - 70 \, A B c}{a^{5}}}\right ) + 4 \, {\left (15 \, B c x^{3} + 7 \, A c x^{2} + 12 \, B a x + 4 \, A a\right )} \sqrt {x}}{24 \, {\left (a^{2} c x^{4} + a^{3} x^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 291, normalized size = 0.92 \begin {gather*} -\frac {B c x^{\frac {3}{2}} + A c \sqrt {x}}{2 \, {\left (c x^{2} + a\right )} a^{2}} - \frac {2 \, {\left (3 \, B x + A\right )}}{3 \, a^{2} x^{\frac {3}{2}}} - \frac {\sqrt {2} {\left (7 \, \left (a c^{3}\right )^{\frac {1}{4}} A c^{2} + 5 \, \left (a c^{3}\right )^{\frac {3}{4}} B\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} \left (\frac {a}{c}\right )^{\frac {1}{4}} + 2 \, \sqrt {x}\right )}}{2 \, \left (\frac {a}{c}\right )^{\frac {1}{4}}}\right )}{8 \, a^{3} c^{2}} - \frac {\sqrt {2} {\left (7 \, \left (a c^{3}\right )^{\frac {1}{4}} A c^{2} + 5 \, \left (a c^{3}\right )^{\frac {3}{4}} B\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} \left (\frac {a}{c}\right )^{\frac {1}{4}} - 2 \, \sqrt {x}\right )}}{2 \, \left (\frac {a}{c}\right )^{\frac {1}{4}}}\right )}{8 \, a^{3} c^{2}} - \frac {\sqrt {2} {\left (7 \, \left (a c^{3}\right )^{\frac {1}{4}} A c^{2} - 5 \, \left (a c^{3}\right )^{\frac {3}{4}} B\right )} \log \left (\sqrt {2} \sqrt {x} \left (\frac {a}{c}\right )^{\frac {1}{4}} + x + \sqrt {\frac {a}{c}}\right )}{16 \, a^{3} c^{2}} + \frac {\sqrt {2} {\left (7 \, \left (a c^{3}\right )^{\frac {1}{4}} A c^{2} - 5 \, \left (a c^{3}\right )^{\frac {3}{4}} B\right )} \log \left (-\sqrt {2} \sqrt {x} \left (\frac {a}{c}\right )^{\frac {1}{4}} + x + \sqrt {\frac {a}{c}}\right )}{16 \, a^{3} c^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 327, normalized size = 1.03 \begin {gather*} -\frac {B c \,x^{\frac {3}{2}}}{2 \left (c \,x^{2}+a \right ) a^{2}}-\frac {A c \sqrt {x}}{2 \left (c \,x^{2}+a \right ) a^{2}}-\frac {7 \left (\frac {a}{c}\right )^{\frac {1}{4}} \sqrt {2}\, A c \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{c}\right )^{\frac {1}{4}}}-1\right )}{8 a^{3}}-\frac {7 \left (\frac {a}{c}\right )^{\frac {1}{4}} \sqrt {2}\, A c \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{c}\right )^{\frac {1}{4}}}+1\right )}{8 a^{3}}-\frac {7 \left (\frac {a}{c}\right )^{\frac {1}{4}} \sqrt {2}\, A c \ln \left (\frac {x +\left (\frac {a}{c}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{c}}}{x -\left (\frac {a}{c}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{c}}}\right )}{16 a^{3}}-\frac {5 \sqrt {2}\, B \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{c}\right )^{\frac {1}{4}}}-1\right )}{8 \left (\frac {a}{c}\right )^{\frac {1}{4}} a^{2}}-\frac {5 \sqrt {2}\, B \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{c}\right )^{\frac {1}{4}}}+1\right )}{8 \left (\frac {a}{c}\right )^{\frac {1}{4}} a^{2}}-\frac {5 \sqrt {2}\, B \ln \left (\frac {x -\left (\frac {a}{c}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{c}}}{x +\left (\frac {a}{c}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{c}}}\right )}{16 \left (\frac {a}{c}\right )^{\frac {1}{4}} a^{2}}-\frac {2 B}{a^{2} \sqrt {x}}-\frac {2 A}{3 a^{2} x^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.24, size = 280, normalized size = 0.88 \begin {gather*} -\frac {15 \, B c x^{3} + 7 \, A c x^{2} + 12 \, B a x + 4 \, A a}{6 \, {\left (a^{2} c x^{\frac {7}{2}} + a^{3} x^{\frac {3}{2}}\right )}} - \frac {c {\left (\frac {2 \, \sqrt {2} {\left (5 \, B \sqrt {a} + 7 \, A \sqrt {c}\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} c^{\frac {1}{4}} + 2 \, \sqrt {c} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {c}}}\right )}{\sqrt {a} \sqrt {\sqrt {a} \sqrt {c}} \sqrt {c}} + \frac {2 \, \sqrt {2} {\left (5 \, B \sqrt {a} + 7 \, A \sqrt {c}\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} c^{\frac {1}{4}} - 2 \, \sqrt {c} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {c}}}\right )}{\sqrt {a} \sqrt {\sqrt {a} \sqrt {c}} \sqrt {c}} - \frac {\sqrt {2} {\left (5 \, B \sqrt {a} - 7 \, A \sqrt {c}\right )} \log \left (\sqrt {2} a^{\frac {1}{4}} c^{\frac {1}{4}} \sqrt {x} + \sqrt {c} x + \sqrt {a}\right )}{a^{\frac {3}{4}} c^{\frac {3}{4}}} + \frac {\sqrt {2} {\left (5 \, B \sqrt {a} - 7 \, A \sqrt {c}\right )} \log \left (-\sqrt {2} a^{\frac {1}{4}} c^{\frac {1}{4}} \sqrt {x} + \sqrt {c} x + \sqrt {a}\right )}{a^{\frac {3}{4}} c^{\frac {3}{4}}}\right )}}{16 \, a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 638, normalized size = 2.01 \begin {gather*} -\frac {\frac {2\,A}{3\,a}+\frac {2\,B\,x}{a}+\frac {7\,A\,c\,x^2}{6\,a^2}+\frac {5\,B\,c\,x^3}{2\,a^2}}{a\,x^{3/2}+c\,x^{7/2}}-2\,\mathrm {atanh}\left (\frac {3136\,A^2\,a^6\,c^5\,\sqrt {x}\,\sqrt {\frac {49\,A^2\,c\,\sqrt {-a^{11}\,c}}{64\,a^{11}}-\frac {25\,B^2\,\sqrt {-a^{11}\,c}}{64\,a^{10}}-\frac {35\,A\,B\,c}{32\,a^5}}}{1000\,B^3\,a^5\,c^4+\frac {2744\,A^3\,c^5\,\sqrt {-a^{11}\,c}}{a^2}-1960\,A^2\,B\,a^4\,c^5-\frac {1400\,A\,B^2\,c^4\,\sqrt {-a^{11}\,c}}{a}}-\frac {1600\,B^2\,a^7\,c^4\,\sqrt {x}\,\sqrt {\frac {49\,A^2\,c\,\sqrt {-a^{11}\,c}}{64\,a^{11}}-\frac {25\,B^2\,\sqrt {-a^{11}\,c}}{64\,a^{10}}-\frac {35\,A\,B\,c}{32\,a^5}}}{1000\,B^3\,a^5\,c^4+\frac {2744\,A^3\,c^5\,\sqrt {-a^{11}\,c}}{a^2}-1960\,A^2\,B\,a^4\,c^5-\frac {1400\,A\,B^2\,c^4\,\sqrt {-a^{11}\,c}}{a}}\right )\,\sqrt {-\frac {25\,B^2\,a\,\sqrt {-a^{11}\,c}-49\,A^2\,c\,\sqrt {-a^{11}\,c}+70\,A\,B\,a^6\,c}{64\,a^{11}}}-2\,\mathrm {atanh}\left (\frac {3136\,A^2\,a^6\,c^5\,\sqrt {x}\,\sqrt {\frac {25\,B^2\,\sqrt {-a^{11}\,c}}{64\,a^{10}}-\frac {49\,A^2\,c\,\sqrt {-a^{11}\,c}}{64\,a^{11}}-\frac {35\,A\,B\,c}{32\,a^5}}}{1000\,B^3\,a^5\,c^4-\frac {2744\,A^3\,c^5\,\sqrt {-a^{11}\,c}}{a^2}-1960\,A^2\,B\,a^4\,c^5+\frac {1400\,A\,B^2\,c^4\,\sqrt {-a^{11}\,c}}{a}}-\frac {1600\,B^2\,a^7\,c^4\,\sqrt {x}\,\sqrt {\frac {25\,B^2\,\sqrt {-a^{11}\,c}}{64\,a^{10}}-\frac {49\,A^2\,c\,\sqrt {-a^{11}\,c}}{64\,a^{11}}-\frac {35\,A\,B\,c}{32\,a^5}}}{1000\,B^3\,a^5\,c^4-\frac {2744\,A^3\,c^5\,\sqrt {-a^{11}\,c}}{a^2}-1960\,A^2\,B\,a^4\,c^5+\frac {1400\,A\,B^2\,c^4\,\sqrt {-a^{11}\,c}}{a}}\right )\,\sqrt {-\frac {49\,A^2\,c\,\sqrt {-a^{11}\,c}-25\,B^2\,a\,\sqrt {-a^{11}\,c}+70\,A\,B\,a^6\,c}{64\,a^{11}}} \end {gather*}
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 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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