Optimal. Leaf size=310 \[ \frac {\sqrt [4]{b} (9 A b-5 a B) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4}}-\frac {\sqrt [4]{b} (9 A b-5 a B) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4}}-\frac {\sqrt [4]{b} (9 A b-5 a B) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4}}+\frac {\sqrt [4]{b} (9 A b-5 a B) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{13/4}}+\frac {9 A b-5 a B}{2 a^3 \sqrt {x}}-\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )} \]
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Rubi [A] time = 0.24, antiderivative size = 310, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 9, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.409, Rules used = {457, 325, 329, 297, 1162, 617, 204, 1165, 628} \begin {gather*} -\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {9 A b-5 a B}{2 a^3 \sqrt {x}}+\frac {\sqrt [4]{b} (9 A b-5 a B) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4}}-\frac {\sqrt [4]{b} (9 A b-5 a B) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4}}-\frac {\sqrt [4]{b} (9 A b-5 a B) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4}}+\frac {\sqrt [4]{b} (9 A b-5 a B) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{13/4}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 204
Rule 297
Rule 325
Rule 329
Rule 457
Rule 617
Rule 628
Rule 1162
Rule 1165
Rubi steps
\begin {align*} \int \frac {A+B x^2}{x^{7/2} \left (a+b x^2\right )^2} \, dx &=\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )}+\frac {\left (\frac {9 A b}{2}-\frac {5 a B}{2}\right ) \int \frac {1}{x^{7/2} \left (a+b x^2\right )} \, dx}{2 a b}\\ &=-\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )}-\frac {(9 A b-5 a B) \int \frac {1}{x^{3/2} \left (a+b x^2\right )} \, dx}{4 a^2}\\ &=-\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {9 A b-5 a B}{2 a^3 \sqrt {x}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )}+\frac {(b (9 A b-5 a B)) \int \frac {\sqrt {x}}{a+b x^2} \, dx}{4 a^3}\\ &=-\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {9 A b-5 a B}{2 a^3 \sqrt {x}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )}+\frac {(b (9 A b-5 a B)) \operatorname {Subst}\left (\int \frac {x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{2 a^3}\\ &=-\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {9 A b-5 a B}{2 a^3 \sqrt {x}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )}-\frac {\left (\sqrt {b} (9 A b-5 a B)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a}-\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{4 a^3}+\frac {\left (\sqrt {b} (9 A b-5 a B)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a}+\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{4 a^3}\\ &=-\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {9 A b-5 a B}{2 a^3 \sqrt {x}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )}+\frac {(9 A b-5 a B) \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {a}}{\sqrt {b}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}+x^2} \, dx,x,\sqrt {x}\right )}{8 a^3}+\frac {(9 A b-5 a B) \operatorname {Subst}\left (\int \frac {1}{\frac {\sqrt {a}}{\sqrt {b}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}+x^2} \, dx,x,\sqrt {x}\right )}{8 a^3}+\frac {\left (\sqrt [4]{b} (9 A b-5 a B)\right ) \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{a}}{\sqrt [4]{b}}+2 x}{-\frac {\sqrt {a}}{\sqrt {b}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}-x^2} \, dx,x,\sqrt {x}\right )}{8 \sqrt {2} a^{13/4}}+\frac {\left (\sqrt [4]{b} (9 A b-5 a B)\right ) \operatorname {Subst}\left (\int \frac {\frac {\sqrt {2} \sqrt [4]{a}}{\sqrt [4]{b}}-2 x}{-\frac {\sqrt {a}}{\sqrt {b}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}-x^2} \, dx,x,\sqrt {x}\right )}{8 \sqrt {2} a^{13/4}}\\ &=-\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {9 A b-5 a B}{2 a^3 \sqrt {x}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )}+\frac {\sqrt [4]{b} (9 A b-5 a B) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4}}-\frac {\sqrt [4]{b} (9 A b-5 a B) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4}}+\frac {\left (\sqrt [4]{b} (9 A b-5 a B)\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4}}-\frac {\left (\sqrt [4]{b} (9 A b-5 a B)\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4}}\\ &=-\frac {9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac {9 A b-5 a B}{2 a^3 \sqrt {x}}+\frac {A b-a B}{2 a b x^{5/2} \left (a+b x^2\right )}-\frac {\sqrt [4]{b} (9 A b-5 a B) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4}}+\frac {\sqrt [4]{b} (9 A b-5 a B) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{13/4}}+\frac {\sqrt [4]{b} (9 A b-5 a B) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4}}-\frac {\sqrt [4]{b} (9 A b-5 a B) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{13/4}}\\ \end {align*}
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Mathematica [C] time = 0.43, size = 151, normalized size = 0.49 \begin {gather*} \frac {2 b x^{3/2} (A b-a B) \, _2F_1\left (\frac {3}{4},2;\frac {7}{4};-\frac {b x^2}{a}\right )}{3 a^4}+\frac {4 A b-2 a B}{a^3 \sqrt {x}}-\frac {2 A}{5 a^2 x^{5/2}}+\frac {\sqrt [4]{b} (a B-2 A b) \tan ^{-1}\left (\frac {\sqrt [4]{b} \sqrt {x}}{\sqrt [4]{-a}}\right )}{(-a)^{13/4}}+\frac {\sqrt [4]{b} (2 A b-a B) \tanh ^{-1}\left (\frac {\sqrt [4]{b} \sqrt {x}}{\sqrt [4]{-a}}\right )}{(-a)^{13/4}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.59, size = 200, normalized size = 0.65 \begin {gather*} \frac {\left (5 a \sqrt [4]{b} B-9 A b^{5/4}\right ) \tan ^{-1}\left (\frac {\sqrt {a}-\sqrt {b} x}{\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}}\right )}{4 \sqrt {2} a^{13/4}}+\frac {\left (5 a \sqrt [4]{b} B-9 A b^{5/4}\right ) \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}}{\sqrt {a}+\sqrt {b} x}\right )}{4 \sqrt {2} a^{13/4}}+\frac {-4 a^2 A-20 a^2 B x^2+36 a A b x^2-25 a b B x^4+45 A b^2 x^4}{10 a^3 x^{5/2} \left (a+b x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.44, size = 974, normalized size = 3.14 \begin {gather*} -\frac {20 \, {\left (a^{3} b x^{5} + a^{4} x^{3}\right )} \left (-\frac {625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right )^{\frac {1}{4}} \arctan \left (\frac {\sqrt {{\left (15625 \, B^{6} a^{6} b^{2} - 168750 \, A B^{5} a^{5} b^{3} + 759375 \, A^{2} B^{4} a^{4} b^{4} - 1822500 \, A^{3} B^{3} a^{3} b^{5} + 2460375 \, A^{4} B^{2} a^{2} b^{6} - 1771470 \, A^{5} B a b^{7} + 531441 \, A^{6} b^{8}\right )} x - {\left (625 \, B^{4} a^{11} b - 4500 \, A B^{3} a^{10} b^{2} + 12150 \, A^{2} B^{2} a^{9} b^{3} - 14580 \, A^{3} B a^{8} b^{4} + 6561 \, A^{4} a^{7} b^{5}\right )} \sqrt {-\frac {625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}}} a^{3} \left (-\frac {625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right )^{\frac {1}{4}} + {\left (125 \, B^{3} a^{6} b - 675 \, A B^{2} a^{5} b^{2} + 1215 \, A^{2} B a^{4} b^{3} - 729 \, A^{3} a^{3} b^{4}\right )} \sqrt {x} \left (-\frac {625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right )^{\frac {1}{4}}}{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}\right ) - 5 \, {\left (a^{3} b x^{5} + a^{4} x^{3}\right )} \left (-\frac {625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right )^{\frac {1}{4}} \log \left (a^{10} \left (-\frac {625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right )^{\frac {3}{4}} - {\left (125 \, B^{3} a^{3} b - 675 \, A B^{2} a^{2} b^{2} + 1215 \, A^{2} B a b^{3} - 729 \, A^{3} b^{4}\right )} \sqrt {x}\right ) + 5 \, {\left (a^{3} b x^{5} + a^{4} x^{3}\right )} \left (-\frac {625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right )^{\frac {1}{4}} \log \left (-a^{10} \left (-\frac {625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right )^{\frac {3}{4}} - {\left (125 \, B^{3} a^{3} b - 675 \, A B^{2} a^{2} b^{2} + 1215 \, A^{2} B a b^{3} - 729 \, A^{3} b^{4}\right )} \sqrt {x}\right ) + 4 \, {\left (5 \, {\left (5 \, B a b - 9 \, A b^{2}\right )} x^{4} + 4 \, A a^{2} + 4 \, {\left (5 \, B a^{2} - 9 \, A a b\right )} x^{2}\right )} \sqrt {x}}{40 \, {\left (a^{3} b x^{5} + a^{4} x^{3}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.54, size = 303, normalized size = 0.98 \begin {gather*} -\frac {B a b x^{\frac {3}{2}} - A b^{2} x^{\frac {3}{2}}}{2 \, {\left (b x^{2} + a\right )} a^{3}} - \frac {\sqrt {2} {\left (5 \, \left (a b^{3}\right )^{\frac {3}{4}} B a - 9 \, \left (a b^{3}\right )^{\frac {3}{4}} A b\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} \left (\frac {a}{b}\right )^{\frac {1}{4}} + 2 \, \sqrt {x}\right )}}{2 \, \left (\frac {a}{b}\right )^{\frac {1}{4}}}\right )}{8 \, a^{4} b^{2}} - \frac {\sqrt {2} {\left (5 \, \left (a b^{3}\right )^{\frac {3}{4}} B a - 9 \, \left (a b^{3}\right )^{\frac {3}{4}} A b\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} \left (\frac {a}{b}\right )^{\frac {1}{4}} - 2 \, \sqrt {x}\right )}}{2 \, \left (\frac {a}{b}\right )^{\frac {1}{4}}}\right )}{8 \, a^{4} b^{2}} + \frac {\sqrt {2} {\left (5 \, \left (a b^{3}\right )^{\frac {3}{4}} B a - 9 \, \left (a b^{3}\right )^{\frac {3}{4}} A b\right )} \log \left (\sqrt {2} \sqrt {x} \left (\frac {a}{b}\right )^{\frac {1}{4}} + x + \sqrt {\frac {a}{b}}\right )}{16 \, a^{4} b^{2}} - \frac {\sqrt {2} {\left (5 \, \left (a b^{3}\right )^{\frac {3}{4}} B a - 9 \, \left (a b^{3}\right )^{\frac {3}{4}} A b\right )} \log \left (-\sqrt {2} \sqrt {x} \left (\frac {a}{b}\right )^{\frac {1}{4}} + x + \sqrt {\frac {a}{b}}\right )}{16 \, a^{4} b^{2}} - \frac {2 \, {\left (5 \, B a x^{2} - 10 \, A b x^{2} + A a\right )}}{5 \, a^{3} x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 339, normalized size = 1.09 \begin {gather*} \frac {A \,b^{2} x^{\frac {3}{2}}}{2 \left (b \,x^{2}+a \right ) a^{3}}-\frac {B b \,x^{\frac {3}{2}}}{2 \left (b \,x^{2}+a \right ) a^{2}}+\frac {9 \sqrt {2}\, A b \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{8 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{3}}+\frac {9 \sqrt {2}\, A b \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{8 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{3}}+\frac {9 \sqrt {2}\, A b \ln \left (\frac {x -\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{b}}}{x +\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{b}}}\right )}{16 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{3}}-\frac {5 \sqrt {2}\, B \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{8 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{2}}-\frac {5 \sqrt {2}\, B \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{8 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{2}}-\frac {5 \sqrt {2}\, B \ln \left (\frac {x -\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{b}}}{x +\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{b}}}\right )}{16 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{2}}+\frac {4 A b}{a^{3} \sqrt {x}}-\frac {2 B}{a^{2} \sqrt {x}}-\frac {2 A}{5 a^{2} x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.31, size = 250, normalized size = 0.81 \begin {gather*} -\frac {5 \, {\left (5 \, B a b - 9 \, A b^{2}\right )} x^{4} + 4 \, A a^{2} + 4 \, {\left (5 \, B a^{2} - 9 \, A a b\right )} x^{2}}{10 \, {\left (a^{3} b x^{\frac {9}{2}} + a^{4} x^{\frac {5}{2}}\right )}} - \frac {{\left (5 \, B a b - 9 \, A b^{2}\right )} {\left (\frac {2 \, \sqrt {2} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} + 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {\sqrt {a} \sqrt {b}} \sqrt {b}} + \frac {2 \, \sqrt {2} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} - 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {\sqrt {a} \sqrt {b}} \sqrt {b}} - \frac {\sqrt {2} \log \left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {1}{4}} b^{\frac {3}{4}}} + \frac {\sqrt {2} \log \left (-\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {1}{4}} b^{\frac {3}{4}}}\right )}}{16 \, a^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 121, normalized size = 0.39 \begin {gather*} \frac {\frac {2\,x^2\,\left (9\,A\,b-5\,B\,a\right )}{5\,a^2}-\frac {2\,A}{5\,a}+\frac {b\,x^4\,\left (9\,A\,b-5\,B\,a\right )}{2\,a^3}}{a\,x^{5/2}+b\,x^{9/2}}+\frac {{\left (-b\right )}^{1/4}\,\mathrm {atan}\left (\frac {{\left (-b\right )}^{1/4}\,\sqrt {x}}{a^{1/4}}\right )\,\left (9\,A\,b-5\,B\,a\right )}{4\,a^{13/4}}-\frac {{\left (-b\right )}^{1/4}\,\mathrm {atanh}\left (\frac {{\left (-b\right )}^{1/4}\,\sqrt {x}}{a^{1/4}}\right )\,\left (9\,A\,b-5\,B\,a\right )}{4\,a^{13/4}} \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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