Optimal. Leaf size=413 \[ -\frac {\log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {a}+\sqrt {b} x^2\right ) \left (-5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{128 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {a}+\sqrt {b} x^2\right ) \left (-5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{128 \sqrt {2} a^{11/4} b^{5/4}}-\frac {\tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}\right ) \left (5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}+1\right ) \left (5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {(a h+3 b d) \tan ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )}{16 a^{5/2} b^{3/2}}-\frac {4 a f-x \left (2 x (a h+3 b d)+a g+7 b c+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {x \left (x (b d-a h)-a g+b c+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2} \]
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Rubi [A] time = 0.49, antiderivative size = 413, normalized size of antiderivative = 1.00, number of steps used = 15, number of rules used = 11, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.314, Rules used = {1858, 1854, 1876, 275, 205, 1168, 1162, 617, 204, 1165, 628} \[ -\frac {\log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {a}+\sqrt {b} x^2\right ) \left (-5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{128 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {a}+\sqrt {b} x^2\right ) \left (-5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{128 \sqrt {2} a^{11/4} b^{5/4}}-\frac {\tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}\right ) \left (5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}+1\right ) \left (5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {(a h+3 b d) \tan ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )}{16 a^{5/2} b^{3/2}}-\frac {4 a f-x \left (2 x (a h+3 b d)+a g+7 b c+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {x \left (x (b d-a h)-a g+b c+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2} \]
Antiderivative was successfully verified.
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Rule 204
Rule 205
Rule 275
Rule 617
Rule 628
Rule 1162
Rule 1165
Rule 1168
Rule 1854
Rule 1858
Rule 1876
Rubi steps
\begin {align*} \int \frac {c+d x+e x^2+f x^3+g x^4+h x^5}{\left (a+b x^4\right )^3} \, dx &=\frac {x \left (b c-a g+(b d-a h) x+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2}-\frac {\int \frac {-b (7 b c+a g)-2 b (3 b d+a h) x-5 b^2 e x^2-4 b^2 f x^3}{\left (a+b x^4\right )^2} \, dx}{8 a b^2}\\ &=\frac {x \left (b c-a g+(b d-a h) x+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2}-\frac {4 a f-x \left (7 b c+a g+2 (3 b d+a h) x+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {\int \frac {3 b (7 b c+a g)+4 b (3 b d+a h) x+5 b^2 e x^2}{a+b x^4} \, dx}{32 a^2 b^2}\\ &=\frac {x \left (b c-a g+(b d-a h) x+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2}-\frac {4 a f-x \left (7 b c+a g+2 (3 b d+a h) x+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {\int \left (\frac {4 b (3 b d+a h) x}{a+b x^4}+\frac {3 b (7 b c+a g)+5 b^2 e x^2}{a+b x^4}\right ) \, dx}{32 a^2 b^2}\\ &=\frac {x \left (b c-a g+(b d-a h) x+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2}-\frac {4 a f-x \left (7 b c+a g+2 (3 b d+a h) x+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {\int \frac {3 b (7 b c+a g)+5 b^2 e x^2}{a+b x^4} \, dx}{32 a^2 b^2}+\frac {(3 b d+a h) \int \frac {x}{a+b x^4} \, dx}{8 a^2 b}\\ &=\frac {x \left (b c-a g+(b d-a h) x+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2}-\frac {4 a f-x \left (7 b c+a g+2 (3 b d+a h) x+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {\left (21 b c-5 \sqrt {a} \sqrt {b} e+3 a g\right ) \int \frac {\sqrt {a} \sqrt {b}-b x^2}{a+b x^4} \, dx}{64 a^{5/2} b^{3/2}}+\frac {\left (21 b c+5 \sqrt {a} \sqrt {b} e+3 a g\right ) \int \frac {\sqrt {a} \sqrt {b}+b x^2}{a+b x^4} \, dx}{64 a^{5/2} b^{3/2}}+\frac {(3 b d+a h) \operatorname {Subst}\left (\int \frac {1}{a+b x^2} \, dx,x,x^2\right )}{16 a^2 b}\\ &=\frac {x \left (b c-a g+(b d-a h) x+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2}-\frac {4 a f-x \left (7 b c+a g+2 (3 b d+a h) x+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {(3 b d+a h) \tan ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )}{16 a^{5/2} b^{3/2}}-\frac {\left (21 b c-5 \sqrt {a} \sqrt {b} e+3 a g\right ) \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}{128 \sqrt {2} a^{11/4} b^{5/4}}-\frac {\left (21 b c-5 \sqrt {a} \sqrt {b} e+3 a g\right ) \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}{128 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\left (21 b c+5 \sqrt {a} \sqrt {b} e+3 a g\right ) \int \frac {1}{\frac {\sqrt {a}}{\sqrt {b}}-\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}+x^2} \, dx}{128 a^{5/2} b^{3/2}}+\frac {\left (21 b c+5 \sqrt {a} \sqrt {b} e+3 a g\right ) \int \frac {1}{\frac {\sqrt {a}}{\sqrt {b}}+\frac {\sqrt {2} \sqrt [4]{a} x}{\sqrt [4]{b}}+x^2} \, dx}{128 a^{5/2} b^{3/2}}\\ &=\frac {x \left (b c-a g+(b d-a h) x+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2}-\frac {4 a f-x \left (7 b c+a g+2 (3 b d+a h) x+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {(3 b d+a h) \tan ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )}{16 a^{5/2} b^{3/2}}-\frac {\left (21 b c-5 \sqrt {a} \sqrt {b} e+3 a g\right ) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {b} x^2\right )}{128 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\left (21 b c-5 \sqrt {a} \sqrt {b} e+3 a g\right ) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {b} x^2\right )}{128 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\left (21 b c+5 \sqrt {a} \sqrt {b} e+3 a g\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}-\frac {\left (21 b c+5 \sqrt {a} \sqrt {b} e+3 a g\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}\\ &=\frac {x \left (b c-a g+(b d-a h) x+b e x^2+b f x^3\right )}{8 a b \left (a+b x^4\right )^2}-\frac {4 a f-x \left (7 b c+a g+2 (3 b d+a h) x+5 b e x^2\right )}{32 a^2 b \left (a+b x^4\right )}+\frac {(3 b d+a h) \tan ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )}{16 a^{5/2} b^{3/2}}-\frac {\left (21 b c+5 \sqrt {a} \sqrt {b} e+3 a g\right ) \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\left (21 b c+5 \sqrt {a} \sqrt {b} e+3 a g\right ) \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}\right )}{64 \sqrt {2} a^{11/4} b^{5/4}}-\frac {\left (21 b c-5 \sqrt {a} \sqrt {b} e+3 a g\right ) \log \left (\sqrt {a}-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {b} x^2\right )}{128 \sqrt {2} a^{11/4} b^{5/4}}+\frac {\left (21 b c-5 \sqrt {a} \sqrt {b} e+3 a g\right ) \log \left (\sqrt {a}+\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {b} x^2\right )}{128 \sqrt {2} a^{11/4} b^{5/4}}\\ \end {align*}
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Mathematica [A] time = 0.43, size = 411, normalized size = 1.00 \[ \frac {-2 \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}\right ) \left (8 a^{5/4} h+5 \sqrt {2} \sqrt {a} b^{3/4} e+24 \sqrt [4]{a} b d+3 \sqrt {2} a \sqrt [4]{b} g+21 \sqrt {2} b^{5/4} c\right )+2 \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{b} x}{\sqrt [4]{a}}+1\right ) \left (-8 a^{5/4} h+5 \sqrt {2} \sqrt {a} b^{3/4} e-24 \sqrt [4]{a} b d+3 \sqrt {2} a \sqrt [4]{b} g+21 \sqrt {2} b^{5/4} c\right )-\frac {32 a^{7/4} \sqrt {b} (a (f+x (g+h x))-b x (c+x (d+e x)))}{\left (a+b x^4\right )^2}+\frac {8 a^{3/4} \sqrt {b} x (a (g+2 h x)+7 b c+b x (6 d+5 e x))}{a+b x^4}+\sqrt {2} \sqrt [4]{b} \log \left (-\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {a}+\sqrt {b} x^2\right ) \left (5 \sqrt {a} \sqrt {b} e-3 a g-21 b c\right )+\sqrt {2} \sqrt [4]{b} \log \left (\sqrt {2} \sqrt [4]{a} \sqrt [4]{b} x+\sqrt {a}+\sqrt {b} x^2\right ) \left (-5 \sqrt {a} \sqrt {b} e+3 a g+21 b c\right )}{256 a^{11/4} b^{3/2}} \]
Antiderivative was successfully verified.
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fricas [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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giac [A] time = 0.20, size = 459, normalized size = 1.11 \[ \frac {\sqrt {2} {\left (12 \, \sqrt {2} \sqrt {a b} b^{2} d + 4 \, \sqrt {2} \sqrt {a b} a b h + 21 \, \left (a b^{3}\right )^{\frac {1}{4}} b^{2} c + 3 \, \left (a b^{3}\right )^{\frac {1}{4}} a b g + 5 \, \left (a b^{3}\right )^{\frac {3}{4}} e\right )} \arctan \left (\frac {\sqrt {2} {\left (2 \, x + \sqrt {2} \left (\frac {a}{b}\right )^{\frac {1}{4}}\right )}}{2 \, \left (\frac {a}{b}\right )^{\frac {1}{4}}}\right )}{128 \, a^{3} b^{3}} + \frac {\sqrt {2} {\left (12 \, \sqrt {2} \sqrt {a b} b^{2} d + 4 \, \sqrt {2} \sqrt {a b} a b h + 21 \, \left (a b^{3}\right )^{\frac {1}{4}} b^{2} c + 3 \, \left (a b^{3}\right )^{\frac {1}{4}} a b g + 5 \, \left (a b^{3}\right )^{\frac {3}{4}} e\right )} \arctan \left (\frac {\sqrt {2} {\left (2 \, x - \sqrt {2} \left (\frac {a}{b}\right )^{\frac {1}{4}}\right )}}{2 \, \left (\frac {a}{b}\right )^{\frac {1}{4}}}\right )}{128 \, a^{3} b^{3}} + \frac {\sqrt {2} {\left (21 \, \left (a b^{3}\right )^{\frac {1}{4}} b^{2} c + 3 \, \left (a b^{3}\right )^{\frac {1}{4}} a b g - 5 \, \left (a b^{3}\right )^{\frac {3}{4}} e\right )} \log \left (x^{2} + \sqrt {2} x \left (\frac {a}{b}\right )^{\frac {1}{4}} + \sqrt {\frac {a}{b}}\right )}{256 \, a^{3} b^{3}} - \frac {\sqrt {2} {\left (21 \, \left (a b^{3}\right )^{\frac {1}{4}} b^{2} c + 3 \, \left (a b^{3}\right )^{\frac {1}{4}} a b g - 5 \, \left (a b^{3}\right )^{\frac {3}{4}} e\right )} \log \left (x^{2} - \sqrt {2} x \left (\frac {a}{b}\right )^{\frac {1}{4}} + \sqrt {\frac {a}{b}}\right )}{256 \, a^{3} b^{3}} + \frac {5 \, b^{2} x^{7} e + 6 \, b^{2} d x^{6} + 2 \, a b h x^{6} + 7 \, b^{2} c x^{5} + a b g x^{5} + 9 \, a b x^{3} e + 10 \, a b d x^{2} - 2 \, a^{2} h x^{2} + 11 \, a b c x - 3 \, a^{2} g x - 4 \, a^{2} f}{32 \, {\left (b x^{4} + a\right )}^{2} a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 561, normalized size = 1.36 \[ \frac {h \arctan \left (\sqrt {\frac {b}{a}}\, x^{2}\right )}{16 \sqrt {a b}\, a b}+\frac {3 d \arctan \left (\sqrt {\frac {b}{a}}\, x^{2}\right )}{16 \sqrt {a b}\, a^{2}}+\frac {5 \sqrt {2}\, e \arctan \left (\frac {\sqrt {2}\, x}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{128 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{2} b}+\frac {5 \sqrt {2}\, e \arctan \left (\frac {\sqrt {2}\, x}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{128 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{2} b}+\frac {5 \sqrt {2}\, e \ln \left (\frac {x^{2}-\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, x +\sqrt {\frac {a}{b}}}{x^{2}+\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, x +\sqrt {\frac {a}{b}}}\right )}{256 \left (\frac {a}{b}\right )^{\frac {1}{4}} a^{2} b}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, g \arctan \left (\frac {\sqrt {2}\, x}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{128 a^{2} b}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, g \arctan \left (\frac {\sqrt {2}\, x}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{128 a^{2} b}+\frac {3 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, g \ln \left (\frac {x^{2}+\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, x +\sqrt {\frac {a}{b}}}{x^{2}-\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, x +\sqrt {\frac {a}{b}}}\right )}{256 a^{2} b}+\frac {21 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c \arctan \left (\frac {\sqrt {2}\, x}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}-1\right )}{128 a^{3}}+\frac {21 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c \arctan \left (\frac {\sqrt {2}\, x}{\left (\frac {a}{b}\right )^{\frac {1}{4}}}+1\right )}{128 a^{3}}+\frac {21 \left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, c \ln \left (\frac {x^{2}+\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, x +\sqrt {\frac {a}{b}}}{x^{2}-\left (\frac {a}{b}\right )^{\frac {1}{4}} \sqrt {2}\, x +\sqrt {\frac {a}{b}}}\right )}{256 a^{3}}+\frac {\frac {5 b e \,x^{7}}{32 a^{2}}+\frac {\left (a h +3 b d \right ) x^{6}}{16 a^{2}}+\frac {9 e \,x^{3}}{32 a}+\frac {\left (a g +7 b c \right ) x^{5}}{32 a^{2}}-\frac {\left (a h -5 b d \right ) x^{2}}{16 a b}-\frac {f}{8 b}-\frac {\left (3 a g -11 b c \right ) x}{32 a b}}{\left (b \,x^{4}+a \right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 3.07, size = 446, normalized size = 1.08 \[ \frac {5 \, b^{2} e x^{7} + 2 \, {\left (3 \, b^{2} d + a b h\right )} x^{6} + 9 \, a b e x^{3} + {\left (7 \, b^{2} c + a b g\right )} x^{5} - 4 \, a^{2} f + 2 \, {\left (5 \, a b d - a^{2} h\right )} x^{2} + {\left (11 \, a b c - 3 \, a^{2} g\right )} x}{32 \, {\left (a^{2} b^{3} x^{8} + 2 \, a^{3} b^{2} x^{4} + a^{4} b\right )}} + \frac {\frac {\sqrt {2} {\left (21 \, b^{\frac {3}{2}} c - 5 \, \sqrt {a} b e + 3 \, a \sqrt {b} g\right )} \log \left (\sqrt {b} x^{2} + \sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} x + \sqrt {a}\right )}{a^{\frac {3}{4}} b^{\frac {3}{4}}} - \frac {\sqrt {2} {\left (21 \, b^{\frac {3}{2}} c - 5 \, \sqrt {a} b e + 3 \, a \sqrt {b} g\right )} \log \left (\sqrt {b} x^{2} - \sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}} x + \sqrt {a}\right )}{a^{\frac {3}{4}} b^{\frac {3}{4}}} + \frac {2 \, {\left (21 \, \sqrt {2} a^{\frac {1}{4}} b^{\frac {7}{4}} c + 5 \, \sqrt {2} a^{\frac {3}{4}} b^{\frac {5}{4}} e + 3 \, \sqrt {2} a^{\frac {5}{4}} b^{\frac {3}{4}} g - 24 \, \sqrt {a} b^{\frac {3}{2}} d - 8 \, a^{\frac {3}{2}} \sqrt {b} h\right )} \arctan \left (\frac {\sqrt {2} {\left (2 \, \sqrt {b} x + \sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{a^{\frac {3}{4}} \sqrt {\sqrt {a} \sqrt {b}} b^{\frac {3}{4}}} + \frac {2 \, {\left (21 \, \sqrt {2} a^{\frac {1}{4}} b^{\frac {7}{4}} c + 5 \, \sqrt {2} a^{\frac {3}{4}} b^{\frac {5}{4}} e + 3 \, \sqrt {2} a^{\frac {5}{4}} b^{\frac {3}{4}} g + 24 \, \sqrt {a} b^{\frac {3}{2}} d + 8 \, a^{\frac {3}{2}} \sqrt {b} h\right )} \arctan \left (\frac {\sqrt {2} {\left (2 \, \sqrt {b} x - \sqrt {2} a^{\frac {1}{4}} b^{\frac {1}{4}}\right )}}{2 \, \sqrt {\sqrt {a} \sqrt {b}}}\right )}{a^{\frac {3}{4}} \sqrt {\sqrt {a} \sqrt {b}} b^{\frac {3}{4}}}}{256 \, a^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.69, size = 1686, normalized size = 4.08 \[ \text {result too large to display} \]
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 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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