Optimal. Leaf size=340 \[ -\frac {3 (b c-a d)^2 (3 a d+b c) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{7/4} b^{13/4}}+\frac {3 (b c-a d)^2 (3 a d+b c) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{7/4} b^{13/4}}-\frac {3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{7/4} b^{13/4}}+\frac {3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{7/4} b^{13/4}}+\frac {2 d^2 \sqrt {x} (3 b c-2 a d)}{b^3}+\frac {\sqrt {x} (b c-a d)^3}{2 a b^3 \left (a+b x^2\right )}+\frac {2 d^3 x^{5/2}}{5 b^2} \]
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Rubi [A] time = 0.39, antiderivative size = 340, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 9, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.375, Rules used = {466, 390, 385, 211, 1165, 628, 1162, 617, 204} \begin {gather*} -\frac {3 (b c-a d)^2 (3 a d+b c) \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{7/4} b^{13/4}}+\frac {3 (b c-a d)^2 (3 a d+b c) \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {a}+\sqrt {b} x\right )}{8 \sqrt {2} a^{7/4} b^{13/4}}-\frac {3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{7/4} b^{13/4}}+\frac {3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}+1\right )}{4 \sqrt {2} a^{7/4} b^{13/4}}+\frac {2 d^2 \sqrt {x} (3 b c-2 a d)}{b^3}+\frac {\sqrt {x} (b c-a d)^3}{2 a b^3 \left (a+b x^2\right )}+\frac {2 d^3 x^{5/2}}{5 b^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 204
Rule 211
Rule 385
Rule 390
Rule 466
Rule 617
Rule 628
Rule 1162
Rule 1165
Rubi steps
\begin {align*} \int \frac {\left (c+d x^2\right )^3}{\sqrt {x} \left (a+b x^2\right )^2} \, dx &=2 \operatorname {Subst}\left (\int \frac {\left (c+d x^4\right )^3}{\left (a+b x^4\right )^2} \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (\frac {d^2 (3 b c-2 a d)}{b^3}+\frac {d^3 x^4}{b^2}+\frac {(b c-a d)^2 (b c+2 a d)+3 b d (b c-a d)^2 x^4}{b^3 \left (a+b x^4\right )^2}\right ) \, dx,x,\sqrt {x}\right )\\ &=\frac {2 d^2 (3 b c-2 a d) \sqrt {x}}{b^3}+\frac {2 d^3 x^{5/2}}{5 b^2}+\frac {2 \operatorname {Subst}\left (\int \frac {(b c-a d)^2 (b c+2 a d)+3 b d (b c-a d)^2 x^4}{\left (a+b x^4\right )^2} \, dx,x,\sqrt {x}\right )}{b^3}\\ &=\frac {2 d^2 (3 b c-2 a d) \sqrt {x}}{b^3}+\frac {2 d^3 x^{5/2}}{5 b^2}+\frac {(b c-a d)^3 \sqrt {x}}{2 a b^3 \left (a+b x^2\right )}+\frac {\left (3 (b c-a d)^2 (b c+3 a d)\right ) \operatorname {Subst}\left (\int \frac {1}{a+b x^4} \, dx,x,\sqrt {x}\right )}{2 a b^3}\\ &=\frac {2 d^2 (3 b c-2 a d) \sqrt {x}}{b^3}+\frac {2 d^3 x^{5/2}}{5 b^2}+\frac {(b c-a d)^3 \sqrt {x}}{2 a b^3 \left (a+b x^2\right )}+\frac {\left (3 (b c-a d)^2 (b c+3 a d)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a}-\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{4 a^{3/2} b^3}+\frac {\left (3 (b c-a d)^2 (b c+3 a d)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a}+\sqrt {b} x^2}{a+b x^4} \, dx,x,\sqrt {x}\right )}{4 a^{3/2} b^3}\\ &=\frac {2 d^2 (3 b c-2 a d) \sqrt {x}}{b^3}+\frac {2 d^3 x^{5/2}}{5 b^2}+\frac {(b c-a d)^3 \sqrt {x}}{2 a b^3 \left (a+b x^2\right )}+\frac {\left (3 (b c-a d)^2 (b c+3 a d)\right ) \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^{3/2} b^{7/2}}+\frac {\left (3 (b c-a d)^2 (b c+3 a d)\right ) \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^{3/2} b^{7/2}}-\frac {\left (3 (b c-a d)^2 (b c+3 a d)\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^{7/4} b^{13/4}}-\frac {\left (3 (b c-a d)^2 (b c+3 a d)\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^{7/4} b^{13/4}}\\ &=\frac {2 d^2 (3 b c-2 a d) \sqrt {x}}{b^3}+\frac {2 d^3 x^{5/2}}{5 b^2}+\frac {(b c-a d)^3 \sqrt {x}}{2 a b^3 \left (a+b x^2\right )}-\frac {3 (b c-a d)^2 (b c+3 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{7/4} b^{13/4}}+\frac {3 (b c-a d)^2 (b c+3 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{7/4} b^{13/4}}+\frac {\left (3 (b c-a d)^2 (b c+3 a d)\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^{7/4} b^{13/4}}-\frac {\left (3 (b c-a d)^2 (b c+3 a d)\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^{7/4} b^{13/4}}\\ &=\frac {2 d^2 (3 b c-2 a d) \sqrt {x}}{b^3}+\frac {2 d^3 x^{5/2}}{5 b^2}+\frac {(b c-a d)^3 \sqrt {x}}{2 a b^3 \left (a+b x^2\right )}-\frac {3 (b c-a d)^2 (b c+3 a d) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{7/4} b^{13/4}}+\frac {3 (b c-a d)^2 (b c+3 a d) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} \sqrt {x}}{\sqrt [4]{a}}\right )}{4 \sqrt {2} a^{7/4} b^{13/4}}-\frac {3 (b c-a d)^2 (b c+3 a d) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{7/4} b^{13/4}}+\frac {3 (b c-a d)^2 (b c+3 a d) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}+\sqrt {b} x\right )}{8 \sqrt {2} a^{7/4} b^{13/4}}\\ \end {align*}
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Mathematica [C] time = 2.64, size = 358, normalized size = 1.05 \begin {gather*} \frac {a \left (45 a^2 \left (28561 c^3+85683 c^2 d x^2+85683 c d^2 x^4+25105 d^3 x^6\right )+18 a b x^2 \left (34927 c^3+104781 c^2 d x^2+119181 c d^2 x^4+36655 d^3 x^6\right )+b^2 x^4 \left (50033 c^3+98259 c^2 d x^2+98259 c d^2 x^4+32753 d^3 x^6\right )\right )-45 \, _2F_1\left (\frac {1}{4},1;\frac {5}{4};-\frac {b x^2}{a}\right ) \left (a^3 \left (28561 c^3+85683 c^2 d x^2+85683 c d^2 x^4+25105 d^3 x^6\right )+9 a^2 b x^2 \left (2187 c^3+6561 c^2 d x^2+7201 c d^2 x^4+2187 d^3 x^6\right )+3 a b^2 x^4 \left (625 c^3+1491 c^2 d x^2+1875 c d^2 x^4+625 d^3 x^6\right )+b^3 x^6 \left (-1151 c^3+3 c^2 d x^2+3 c d^2 x^4+d^3 x^6\right )\right )}{34560 a^2 b^3 x^{11/2}}-\frac {128 b x^{5/2} \left (c+d x^2\right )^3 \, _5F_4\left (\frac {5}{4},2,2,2,2;1,1,1,\frac {21}{4};-\frac {b x^2}{a}\right )}{9945 a^3} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [A] time = 0.51, size = 246, normalized size = 0.72 \begin {gather*} -\frac {3 (3 a d+b c) (a d-b c)^2 \tan ^{-1}\left (\frac {\sqrt {a}-\sqrt {b} x}{\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}}\right )}{4 \sqrt {2} a^{7/4} b^{13/4}}+\frac {3 (3 a d+b c) (a d-b c)^2 \tanh ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} \sqrt {x}}{\sqrt {a}+\sqrt {b} x}\right )}{4 \sqrt {2} a^{7/4} b^{13/4}}-\frac {\sqrt {x} \left (45 a^3 d^3-75 a^2 b c d^2+36 a^2 b d^3 x^2+15 a b^2 c^2 d-60 a b^2 c d^2 x^2-4 a b^2 d^3 x^4-5 b^3 c^3\right )}{10 a b^3 \left (a+b x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.37, size = 1944, normalized size = 5.72
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 511, normalized size = 1.50 \begin {gather*} \frac {3 \, \sqrt {2} {\left (\left (a b^{3}\right )^{\frac {1}{4}} b^{3} c^{3} + \left (a b^{3}\right )^{\frac {1}{4}} a b^{2} c^{2} d - 5 \, \left (a b^{3}\right )^{\frac {1}{4}} a^{2} b c d^{2} + 3 \, \left (a b^{3}\right )^{\frac {1}{4}} a^{3} d^{3}\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^{2} b^{4}} + \frac {3 \, \sqrt {2} {\left (\left (a b^{3}\right )^{\frac {1}{4}} b^{3} c^{3} + \left (a b^{3}\right )^{\frac {1}{4}} a b^{2} c^{2} d - 5 \, \left (a b^{3}\right )^{\frac {1}{4}} a^{2} b c d^{2} + 3 \, \left (a b^{3}\right )^{\frac {1}{4}} a^{3} d^{3}\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^{2} b^{4}} + \frac {3 \, \sqrt {2} {\left (\left (a b^{3}\right )^{\frac {1}{4}} b^{3} c^{3} + \left (a b^{3}\right )^{\frac {1}{4}} a b^{2} c^{2} d - 5 \, \left (a b^{3}\right )^{\frac {1}{4}} a^{2} b c d^{2} + 3 \, \left (a b^{3}\right )^{\frac {1}{4}} a^{3} d^{3}\right )} \log \left (\sqrt {2} \sqrt {x} \left (\frac {a}{b}\right )^{\frac {1}{4}} + x + \sqrt {\frac {a}{b}}\right )}{16 \, a^{2} b^{4}} - \frac {3 \, \sqrt {2} {\left (\left (a b^{3}\right )^{\frac {1}{4}} b^{3} c^{3} + \left (a b^{3}\right )^{\frac {1}{4}} a b^{2} c^{2} d - 5 \, \left (a b^{3}\right )^{\frac {1}{4}} a^{2} b c d^{2} + 3 \, \left (a b^{3}\right )^{\frac {1}{4}} a^{3} d^{3}\right )} \log \left (-\sqrt {2} \sqrt {x} \left (\frac {a}{b}\right )^{\frac {1}{4}} + x + \sqrt {\frac {a}{b}}\right )}{16 \, a^{2} b^{4}} + \frac {b^{3} c^{3} \sqrt {x} - 3 \, a b^{2} c^{2} d \sqrt {x} + 3 \, a^{2} b c d^{2} \sqrt {x} - a^{3} d^{3} \sqrt {x}}{2 \, {\left (b x^{2} + a\right )} a b^{3}} + \frac {2 \, {\left (b^{8} d^{3} x^{\frac {5}{2}} + 15 \, b^{8} c d^{2} \sqrt {x} - 10 \, a b^{7} d^{3} \sqrt {x}\right )}}{5 \, b^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 697, normalized size = 2.05 \begin {gather*} \frac {2 d^{3} x^{\frac {5}{2}}}{5 b^{2}}-\frac {a^{2} d^{3} \sqrt {x}}{2 \left (b \,x^{2}+a \right ) b^{3}}+\frac {3 a c \,d^{2} \sqrt {x}}{2 \left (b \,x^{2}+a \right ) b^{2}}+\frac {c^{3} \sqrt {x}}{2 \left (b \,x^{2}+a \right ) a}-\frac {3 c^{2} d \sqrt {x}}{2 \left (b \,x^{2}+a \right ) b}+\frac {9 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, a \,d^{3} \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{8 b^{3}}+\frac {9 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, a \,d^{3} \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{8 b^{3}}+\frac {9 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, a \,d^{3} \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 b^{3}}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c^{2} d \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{8 a b}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c^{2} d \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{8 a b}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c^{2} d \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 a b}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c^{3} \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{8 a^{2}}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c^{3} \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{8 a^{2}}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c^{3} \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 a^{2}}-\frac {15 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c \,d^{2} \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{8 b^{2}}-\frac {15 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c \,d^{2} \arctan \left (\frac {\sqrt {2}\, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{8 b^{2}}-\frac {15 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c \,d^{2} \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 b^{2}}-\frac {4 a \,d^{3} \sqrt {x}}{b^{3}}+\frac {6 c \,d^{2} \sqrt {x}}{b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.58, size = 412, normalized size = 1.21 \begin {gather*} \frac {{\left (b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right )} \sqrt {x}}{2 \, {\left (a b^{4} x^{2} + a^{2} b^{3}\right )}} + \frac {2 \, {\left (b d^{3} x^{\frac {5}{2}} + 5 \, {\left (3 \, b c d^{2} - 2 \, a d^{3}\right )} \sqrt {x}\right )}}{5 \, b^{3}} + \frac {3 \, {\left (\frac {2 \, \sqrt {2} {\left (b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\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^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\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^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\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^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\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 )}}{16 \, a b^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 1636, normalized size = 4.81
result too large to display
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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