Optimal. Leaf size=293 \[ -\frac {3 (a B+7 A b) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {3 (a B+7 A b) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}-\frac {3 (a B+7 A b) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{32 \sqrt {2} a^{11/4} b^{5/4}}+\frac {3 (a B+7 A b) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{32 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\sqrt {x} (a B+7 A b)}{16 a^2 b \left (a+b x^2\right )}+\frac {\sqrt {x} (A b-a B)}{4 a b \left (a+b x^2\right )^2} \]
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Rubi [A] time = 0.21, antiderivative size = 293, normalized size of antiderivative = 1.00, number of steps used = 12, number of rules used = 9, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.409, Rules used = {457, 290, 329, 211, 1165, 628, 1162, 617, 204} \[ -\frac {3 (a B+7 A b) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {3 (a B+7 A b) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}-\frac {3 (a B+7 A b) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{32 \sqrt {2} a^{11/4} b^{5/4}}+\frac {3 (a B+7 A b) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{32 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\sqrt {x} (a B+7 A b)}{16 a^2 b \left (a+b x^2\right )}+\frac {\sqrt {x} (A b-a B)}{4 a b \left (a+b x^2\right )^2} \]
Antiderivative was successfully verified.
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Rule 204
Rule 211
Rule 290
Rule 329
Rule 457
Rule 617
Rule 628
Rule 1162
Rule 1165
Rubi steps
\begin {align*} \int \frac {A+B x^2}{\sqrt {x} \left (a+b x^2\right )^3} \, dx &=\frac {(A b-a B) \sqrt {x}}{4 a b \left (a+b x^2\right )^2}+\frac {\left (\frac {7 A b}{2}+\frac {a B}{2}\right ) \int \frac {1}{\sqrt {x} \left (a+b x^2\right )^2} \, dx}{4 a b}\\ &=\frac {(A b-a B) \sqrt {x}}{4 a b \left (a+b x^2\right )^2}+\frac {(7 A b+a B) \sqrt {x}}{16 a^2 b \left (a+b x^2\right )}+\frac {(3 (7 A b+a B)) \int \frac {1}{\sqrt {x} \left (a+b x^2\right )} \, dx}{32 a^2 b}\\ &=\frac {(A b-a B) \sqrt {x}}{4 a b \left (a+b x^2\right )^2}+\frac {(7 A b+a B) \sqrt {x}}{16 a^2 b \left (a+b x^2\right )}+\frac {(3 (7 A b+a B)) \operatorname {Subst}\left (\int \frac {1}{a+b x^4} \, dx,x,\sqrt {x}\right )}{16 a^2 b}\\ &=\frac {(A b-a B) \sqrt {x}}{4 a b \left (a+b x^2\right )^2}+\frac {(7 A b+a B) \sqrt {x}}{16 a^2 b \left (a+b x^2\right )}+\frac {(3 (7 A b+a B)) \operatorname {Subst}\left (\int \frac {\sqrt {a}-\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{32 a^{5/2} b}+\frac {(3 (7 A b+a B)) \operatorname {Subst}\left (\int \frac {\sqrt {a}+\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{32 a^{5/2} b}\\ &=\frac {(A b-a B) \sqrt {x}}{4 a b \left (a+b x^2\right )^2}+\frac {(7 A b+a B) \sqrt {x}}{16 a^2 b \left (a+b x^2\right )}+\frac {(3 (7 A b+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 )}{64 a^{5/2} b^{3/2}}+\frac {(3 (7 A b+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 )}{64 a^{5/2} b^{3/2}}-\frac {(3 (7 A b+a B)) \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 )}{64 \sqrt {2} a^{11/4} b^{5/4}}-\frac {(3 (7 A b+a B)) \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 )}{64 \sqrt {2} a^{11/4} b^{5/4}}\\ &=\frac {(A b-a B) \sqrt {x}}{4 a b \left (a+b x^2\right )^2}+\frac {(7 A b+a B) \sqrt {x}}{16 a^2 b \left (a+b x^2\right )}-\frac {3 (7 A b+a B) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {3 (7 A b+a B) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {(3 (7 A b+a B)) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{32 \sqrt {2} a^{11/4} b^{5/4}}-\frac {(3 (7 A b+a B)) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{32 \sqrt {2} a^{11/4} b^{5/4}}\\ &=\frac {(A b-a B) \sqrt {x}}{4 a b \left (a+b x^2\right )^2}+\frac {(7 A b+a B) \sqrt {x}}{16 a^2 b \left (a+b x^2\right )}-\frac {3 (7 A b+a B) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{32 \sqrt {2} a^{11/4} b^{5/4}}+\frac {3 (7 A b+a B) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{32 \sqrt {2} a^{11/4} b^{5/4}}-\frac {3 (7 A b+a B) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {3 (7 A b+a B) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}\\ \end {align*}
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Mathematica [A] time = 0.28, size = 230, normalized size = 0.78 \[ \frac {\frac {(a B+7 A b) \left (7 \left (a+b x^2\right ) \left (8 a^{3/4} \sqrt [4]{b} \sqrt {x}-3 \sqrt {2} \left (a+b x^2\right ) \left (\log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )-\log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )+2 \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )-2 \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )\right )\right )+32 a^{7/4} \sqrt [4]{b} \sqrt {x}\right )}{a^{11/4} \sqrt [4]{b}}-256 B \sqrt {x}}{896 b \left (a+b x^2\right )^2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.53, size = 793, normalized size = 2.71 \[ \frac {12 \, {\left (a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right )} \left (-\frac {B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right )^{\frac {1}{4}} \arctan \left (\frac {\sqrt {a^{6} b^{2} \sqrt {-\frac {B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}} + {\left (B^{2} a^{2} + 14 \, A B a b + 49 \, A^{2} b^{2}\right )} x} a^{8} b^{4} \left (-\frac {B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right )^{\frac {3}{4}} - {\left (B a^{9} b^{4} + 7 \, A a^{8} b^{5}\right )} \sqrt {x} \left (-\frac {B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right )^{\frac {3}{4}}}{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}\right ) + 3 \, {\left (a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right )} \left (-\frac {B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right )^{\frac {1}{4}} \log \left (3 \, a^{3} b \left (-\frac {B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right )^{\frac {1}{4}} + 3 \, {\left (B a + 7 \, A b\right )} \sqrt {x}\right ) - 3 \, {\left (a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right )} \left (-\frac {B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right )^{\frac {1}{4}} \log \left (-3 \, a^{3} b \left (-\frac {B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right )^{\frac {1}{4}} + 3 \, {\left (B a + 7 \, A b\right )} \sqrt {x}\right ) - 4 \, {\left (3 \, B a^{2} - 11 \, A a b - {\left (B a b + 7 \, A b^{2}\right )} x^{2}\right )} \sqrt {x}}{64 \, {\left (a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.44, size = 293, normalized size = 1.00 \[ \frac {3 \, \sqrt {2} {\left (\left (a b^{3}\right )^{\frac {1}{4}} B a + 7 \, \left (a b^{3}\right )^{\frac {1}{4}} A b\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} \left (\frac {a}{b}\right )^{\frac {1}{4}} + 2 \, \sqrt {x}\right )}}{2 \, \left (\frac {a}{b}\right )^{\frac {1}{4}}}\right )}{64 \, a^{3} b^{2}} + \frac {3 \, \sqrt {2} {\left (\left (a b^{3}\right )^{\frac {1}{4}} B a + 7 \, \left (a b^{3}\right )^{\frac {1}{4}} A b\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} \left (\frac {a}{b}\right )^{\frac {1}{4}} - 2 \, \sqrt {x}\right )}}{2 \, \left (\frac {a}{b}\right )^{\frac {1}{4}}}\right )}{64 \, a^{3} b^{2}} + \frac {3 \, \sqrt {2} {\left (\left (a b^{3}\right )^{\frac {1}{4}} B a + 7 \, \left (a b^{3}\right )^{\frac {1}{4}} A b\right )} \log \left (\sqrt {2} \sqrt {x} \left (\frac {a}{b}\right )^{\frac {1}{4}} + x + \sqrt {\frac {a}{b}}\right )}{128 \, a^{3} b^{2}} - \frac {3 \, \sqrt {2} {\left (\left (a b^{3}\right )^{\frac {1}{4}} B a + 7 \, \left (a b^{3}\right )^{\frac {1}{4}} A b\right )} \log \left (-\sqrt {2} \sqrt {x} \left (\frac {a}{b}\right )^{\frac {1}{4}} + x + \sqrt {\frac {a}{b}}\right )}{128 \, a^{3} b^{2}} + \frac {B a b x^{\frac {5}{2}} + 7 \, A b^{2} x^{\frac {5}{2}} - 3 \, B a^{2} \sqrt {x} + 11 \, A a b \sqrt {x}}{16 \, {\left (b x^{2} + a\right )}^{2} a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 325, normalized size = 1.11 \[ \frac {21 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, A \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{64 a^{3}}+\frac {21 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, A \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{64 a^{3}}+\frac {21 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, A \ln \left (\frac {x +\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{b}}}{x -\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{b}}}\right )}{128 a^{3}}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, B \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{64 a^{2} b}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, B \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{64 a^{2} b}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, B \ln \left (\frac {x +\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{b}}}{x -\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, \sqrt {x}+\sqrt {\frac {a}{b}}}\right )}{128 a^{2} b}+\frac {\frac {\left (7 A b +B a \right ) x^{\frac {5}{2}}}{16 a^{2}}+\frac {\left (11 A b -3 B a \right ) \sqrt {x}}{16 a b}}{\left (b \,x^{2}+a \right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.33, size = 276, normalized size = 0.94 \[ \frac {{\left (B a b + 7 \, A b^{2}\right )} x^{\frac {5}{2}} - {\left (3 \, B a^{2} - 11 \, A a b\right )} \sqrt {x}}{16 \, {\left (a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right )}} + \frac {3 \, {\left (\frac {2 \, \sqrt {2} {\left (B a + 7 \, A b\right )} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} + 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {a} \sqrt {\sqrt {a} \sqrt {b}}} + \frac {2 \, \sqrt {2} {\left (B a + 7 \, A b\right )} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} - 2 \, \sqrt {b} \sqrt {x}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{\sqrt {a} \sqrt {\sqrt {a} \sqrt {b}}} + \frac {\sqrt {2} {\left (B a + 7 \, A b\right )} \log \left (\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {3}{4}} b^{\frac {1}{4}}} - \frac {\sqrt {2} {\left (B a + 7 \, A b\right )} \log \left (-\sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} \sqrt {x} + \sqrt {b} x + \sqrt {a}\right )}{a^{\frac {3}{4}} b^{\frac {1}{4}}}\right )}}{128 \, a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.48, size = 780, normalized size = 2.66 \[ \frac {\frac {x^{5/2}\,\left (7\,A\,b+B\,a\right )}{16\,a^2}+\frac {\sqrt {x}\,\left (11\,A\,b-3\,B\,a\right )}{16\,a\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac {\mathrm {atan}\left (\frac {\frac {\left (7\,A\,b+B\,a\right )\,\left (\frac {9\,\sqrt {x}\,\left (49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right )}{64\,a^4}-\frac {9\,\left (7\,A\,b+B\,a\right )\,\left (7\,A\,b^3+B\,a\,b^2\right )}{64\,{\left (-a\right )}^{15/4}\,b^{5/4}}\right )\,3{}\mathrm {i}}{64\,{\left (-a\right )}^{11/4}\,b^{5/4}}+\frac {\left (7\,A\,b+B\,a\right )\,\left (\frac {9\,\sqrt {x}\,\left (49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right )}{64\,a^4}+\frac {9\,\left (7\,A\,b+B\,a\right )\,\left (7\,A\,b^3+B\,a\,b^2\right )}{64\,{\left (-a\right )}^{15/4}\,b^{5/4}}\right )\,3{}\mathrm {i}}{64\,{\left (-a\right )}^{11/4}\,b^{5/4}}}{\frac {3\,\left (7\,A\,b+B\,a\right )\,\left (\frac {9\,\sqrt {x}\,\left (49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right )}{64\,a^4}-\frac {9\,\left (7\,A\,b+B\,a\right )\,\left (7\,A\,b^3+B\,a\,b^2\right )}{64\,{\left (-a\right )}^{15/4}\,b^{5/4}}\right )}{64\,{\left (-a\right )}^{11/4}\,b^{5/4}}-\frac {3\,\left (7\,A\,b+B\,a\right )\,\left (\frac {9\,\sqrt {x}\,\left (49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right )}{64\,a^4}+\frac {9\,\left (7\,A\,b+B\,a\right )\,\left (7\,A\,b^3+B\,a\,b^2\right )}{64\,{\left (-a\right )}^{15/4}\,b^{5/4}}\right )}{64\,{\left (-a\right )}^{11/4}\,b^{5/4}}}\right )\,\left (7\,A\,b+B\,a\right )\,3{}\mathrm {i}}{32\,{\left (-a\right )}^{11/4}\,b^{5/4}}-\frac {3\,\mathrm {atan}\left (\frac {\frac {3\,\left (7\,A\,b+B\,a\right )\,\left (\frac {9\,\sqrt {x}\,\left (49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right )}{64\,a^4}-\frac {\left (7\,A\,b+B\,a\right )\,\left (7\,A\,b^3+B\,a\,b^2\right )\,9{}\mathrm {i}}{64\,{\left (-a\right )}^{15/4}\,b^{5/4}}\right )}{64\,{\left (-a\right )}^{11/4}\,b^{5/4}}+\frac {3\,\left (7\,A\,b+B\,a\right )\,\left (\frac {9\,\sqrt {x}\,\left (49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right )}{64\,a^4}+\frac {\left (7\,A\,b+B\,a\right )\,\left (7\,A\,b^3+B\,a\,b^2\right )\,9{}\mathrm {i}}{64\,{\left (-a\right )}^{15/4}\,b^{5/4}}\right )}{64\,{\left (-a\right )}^{11/4}\,b^{5/4}}}{\frac {\left (7\,A\,b+B\,a\right )\,\left (\frac {9\,\sqrt {x}\,\left (49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right )}{64\,a^4}-\frac {\left (7\,A\,b+B\,a\right )\,\left (7\,A\,b^3+B\,a\,b^2\right )\,9{}\mathrm {i}}{64\,{\left (-a\right )}^{15/4}\,b^{5/4}}\right )\,3{}\mathrm {i}}{64\,{\left (-a\right )}^{11/4}\,b^{5/4}}-\frac {\left (7\,A\,b+B\,a\right )\,\left (\frac {9\,\sqrt {x}\,\left (49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right )}{64\,a^4}+\frac {\left (7\,A\,b+B\,a\right )\,\left (7\,A\,b^3+B\,a\,b^2\right )\,9{}\mathrm {i}}{64\,{\left (-a\right )}^{15/4}\,b^{5/4}}\right )\,3{}\mathrm {i}}{64\,{\left (-a\right )}^{11/4}\,b^{5/4}}}\right )\,\left (7\,A\,b+B\,a\right )}{32\,{\left (-a\right )}^{11/4}\,b^{5/4}} \]
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 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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