Optimal. Leaf size=198 \[ -\frac {155 b^3 \tan ^{-1}\left (\frac {\sqrt [4]{a} x}{\sqrt [4]{a x^4+b x^3}}\right )}{64 a^{15/4}}+\frac {2 \sqrt [4]{2} b^3 \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} x}{\sqrt [4]{a x^4+b x^3}}\right )}{a^{15/4}}+\frac {155 b^3 \tanh ^{-1}\left (\frac {\sqrt [4]{a} x}{\sqrt [4]{a x^4+b x^3}}\right )}{64 a^{15/4}}-\frac {2 \sqrt [4]{2} b^3 \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} x}{\sqrt [4]{a x^4+b x^3}}\right )}{a^{15/4}}+\frac {\left (32 a^2 x^2+52 a b x+101 b^2\right ) \sqrt [4]{a x^4+b x^3}}{96 a^3} \]
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Rubi [A] time = 0.46, antiderivative size = 339, normalized size of antiderivative = 1.71, number of steps used = 27, number of rules used = 11, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.393, Rules used = {2042, 101, 157, 50, 63, 331, 298, 203, 206, 105, 93} \begin {gather*} -\frac {155 b^3 \sqrt [4]{a x^4+b x^3} \tan ^{-1}\left (\frac {\sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{a x+b}}\right )}{64 a^{15/4} x^{3/4} \sqrt [4]{a x+b}}+\frac {2 \sqrt [4]{2} b^3 \sqrt [4]{a x^4+b x^3} \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{a x+b}}\right )}{a^{15/4} x^{3/4} \sqrt [4]{a x+b}}+\frac {155 b^3 \sqrt [4]{a x^4+b x^3} \tanh ^{-1}\left (\frac {\sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{a x+b}}\right )}{64 a^{15/4} x^{3/4} \sqrt [4]{a x+b}}-\frac {2 \sqrt [4]{2} b^3 \sqrt [4]{a x^4+b x^3} \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{a x+b}}\right )}{a^{15/4} x^{3/4} \sqrt [4]{a x+b}}+\frac {101 b^2 \sqrt [4]{a x^4+b x^3}}{96 a^3}+\frac {13 b x \sqrt [4]{a x^4+b x^3}}{24 a^2}+\frac {x^2 \sqrt [4]{a x^4+b x^3}}{3 a} \end {gather*}
Antiderivative was successfully verified.
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Rule 50
Rule 63
Rule 93
Rule 101
Rule 105
Rule 157
Rule 203
Rule 206
Rule 298
Rule 331
Rule 2042
Rubi steps
\begin {align*} \int \frac {x^2 \sqrt [4]{b x^3+a x^4}}{-b+a x} \, dx &=\frac {\sqrt [4]{b x^3+a x^4} \int \frac {x^{11/4} \sqrt [4]{b+a x}}{-b+a x} \, dx}{x^{3/4} \sqrt [4]{b+a x}}\\ &=\frac {x^2 \sqrt [4]{b x^3+a x^4}}{3 a}-\frac {\sqrt [4]{b x^3+a x^4} \int \frac {x^{7/4} \left (-\frac {11 b^2}{4}-\frac {13 a b x}{4}\right )}{(-b+a x) (b+a x)^{3/4}} \, dx}{3 a x^{3/4} \sqrt [4]{b+a x}}\\ &=\frac {x^2 \sqrt [4]{b x^3+a x^4}}{3 a}+\frac {\left (13 b \sqrt [4]{b x^3+a x^4}\right ) \int \frac {x^{7/4}}{(b+a x)^{3/4}} \, dx}{12 a x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (2 b^2 \sqrt [4]{b x^3+a x^4}\right ) \int \frac {x^{7/4}}{(-b+a x) (b+a x)^{3/4}} \, dx}{a x^{3/4} \sqrt [4]{b+a x}}\\ &=\frac {13 b x \sqrt [4]{b x^3+a x^4}}{24 a^2}+\frac {x^2 \sqrt [4]{b x^3+a x^4}}{3 a}-\frac {\left (91 b^2 \sqrt [4]{b x^3+a x^4}\right ) \int \frac {x^{3/4}}{(b+a x)^{3/4}} \, dx}{96 a^2 x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (2 b^2 \sqrt [4]{b x^3+a x^4}\right ) \int \frac {x^{3/4}}{(b+a x)^{3/4}} \, dx}{a^2 x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (2 b^3 \sqrt [4]{b x^3+a x^4}\right ) \int \frac {x^{3/4}}{(-b+a x) (b+a x)^{3/4}} \, dx}{a^2 x^{3/4} \sqrt [4]{b+a x}}\\ &=\frac {101 b^2 \sqrt [4]{b x^3+a x^4}}{96 a^3}+\frac {13 b x \sqrt [4]{b x^3+a x^4}}{24 a^2}+\frac {x^2 \sqrt [4]{b x^3+a x^4}}{3 a}+\frac {\left (91 b^3 \sqrt [4]{b x^3+a x^4}\right ) \int \frac {1}{\sqrt [4]{x} (b+a x)^{3/4}} \, dx}{128 a^3 x^{3/4} \sqrt [4]{b+a x}}-\frac {\left (3 b^3 \sqrt [4]{b x^3+a x^4}\right ) \int \frac {1}{\sqrt [4]{x} (b+a x)^{3/4}} \, dx}{2 a^3 x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (2 b^3 \sqrt [4]{b x^3+a x^4}\right ) \int \frac {1}{\sqrt [4]{x} (b+a x)^{3/4}} \, dx}{a^3 x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (2 b^4 \sqrt [4]{b x^3+a x^4}\right ) \int \frac {1}{\sqrt [4]{x} (-b+a x) (b+a x)^{3/4}} \, dx}{a^3 x^{3/4} \sqrt [4]{b+a x}}\\ &=\frac {101 b^2 \sqrt [4]{b x^3+a x^4}}{96 a^3}+\frac {13 b x \sqrt [4]{b x^3+a x^4}}{24 a^2}+\frac {x^2 \sqrt [4]{b x^3+a x^4}}{3 a}+\frac {\left (91 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (b+a x^4\right )^{3/4}} \, dx,x,\sqrt [4]{x}\right )}{32 a^3 x^{3/4} \sqrt [4]{b+a x}}-\frac {\left (6 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (b+a x^4\right )^{3/4}} \, dx,x,\sqrt [4]{x}\right )}{a^3 x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (8 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (b+a x^4\right )^{3/4}} \, dx,x,\sqrt [4]{x}\right )}{a^3 x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (8 b^4 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{-b+2 a b x^4} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^3 x^{3/4} \sqrt [4]{b+a x}}\\ &=\frac {101 b^2 \sqrt [4]{b x^3+a x^4}}{96 a^3}+\frac {13 b x \sqrt [4]{b x^3+a x^4}}{24 a^2}+\frac {x^2 \sqrt [4]{b x^3+a x^4}}{3 a}-\frac {\left (2 \sqrt {2} b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{1-\sqrt {2} \sqrt {a} x^2} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{7/2} x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (2 \sqrt {2} b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{1+\sqrt {2} \sqrt {a} x^2} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{7/2} x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (91 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{1-a x^4} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{32 a^3 x^{3/4} \sqrt [4]{b+a x}}-\frac {\left (6 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{1-a x^4} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^3 x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (8 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{1-a x^4} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^3 x^{3/4} \sqrt [4]{b+a x}}\\ &=\frac {101 b^2 \sqrt [4]{b x^3+a x^4}}{96 a^3}+\frac {13 b x \sqrt [4]{b x^3+a x^4}}{24 a^2}+\frac {x^2 \sqrt [4]{b x^3+a x^4}}{3 a}+\frac {2 \sqrt [4]{2} b^3 \sqrt [4]{b x^3+a x^4} \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{15/4} x^{3/4} \sqrt [4]{b+a x}}-\frac {2 \sqrt [4]{2} b^3 \sqrt [4]{b x^3+a x^4} \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{15/4} x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (91 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{1-\sqrt {a} x^2} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{64 a^{7/2} x^{3/4} \sqrt [4]{b+a x}}-\frac {\left (91 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{1+\sqrt {a} x^2} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{64 a^{7/2} x^{3/4} \sqrt [4]{b+a x}}-\frac {\left (3 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{1-\sqrt {a} x^2} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{7/2} x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (3 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{1+\sqrt {a} x^2} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{7/2} x^{3/4} \sqrt [4]{b+a x}}+\frac {\left (4 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{1-\sqrt {a} x^2} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{7/2} x^{3/4} \sqrt [4]{b+a x}}-\frac {\left (4 b^3 \sqrt [4]{b x^3+a x^4}\right ) \operatorname {Subst}\left (\int \frac {1}{1+\sqrt {a} x^2} \, dx,x,\frac {\sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{7/2} x^{3/4} \sqrt [4]{b+a x}}\\ &=\frac {101 b^2 \sqrt [4]{b x^3+a x^4}}{96 a^3}+\frac {13 b x \sqrt [4]{b x^3+a x^4}}{24 a^2}+\frac {x^2 \sqrt [4]{b x^3+a x^4}}{3 a}-\frac {155 b^3 \sqrt [4]{b x^3+a x^4} \tan ^{-1}\left (\frac {\sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{64 a^{15/4} x^{3/4} \sqrt [4]{b+a x}}+\frac {2 \sqrt [4]{2} b^3 \sqrt [4]{b x^3+a x^4} \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{15/4} x^{3/4} \sqrt [4]{b+a x}}+\frac {155 b^3 \sqrt [4]{b x^3+a x^4} \tanh ^{-1}\left (\frac {\sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{64 a^{15/4} x^{3/4} \sqrt [4]{b+a x}}-\frac {2 \sqrt [4]{2} b^3 \sqrt [4]{b x^3+a x^4} \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} \sqrt [4]{x}}{\sqrt [4]{b+a x}}\right )}{a^{15/4} x^{3/4} \sqrt [4]{b+a x}}\\ \end {align*}
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Mathematica [C] time = 0.17, size = 183, normalized size = 0.92 \begin {gather*} \frac {4 x^3 \left (21 a^2 x^2 (a x+b) \, _2F_1\left (-\frac {1}{4},\frac {11}{4};\frac {15}{4};-\frac {a x}{b}\right )+77 b^2 (a x+b) \, _2F_1\left (-\frac {1}{4},\frac {3}{4};\frac {7}{4};-\frac {a x}{b}\right )+77 b^2 \left ((a x+b) \, _2F_1\left (\frac {3}{4},\frac {3}{4};\frac {7}{4};-\frac {a x}{b}\right )-2 b \sqrt [4]{\frac {a x}{b}+1} \, _2F_1\left (\frac {3}{4},1;\frac {7}{4};\frac {2 a x}{b+a x}\right )\right )+33 a b x (a x+b) \, _2F_1\left (-\frac {1}{4},\frac {7}{4};\frac {11}{4};-\frac {a x}{b}\right )\right )}{231 a^3 \left (x^3 (a x+b)\right )^{3/4} \sqrt [4]{\frac {a x}{b}+1}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.82, size = 198, normalized size = 1.00 \begin {gather*} \frac {\left (101 b^2+52 a b x+32 a^2 x^2\right ) \sqrt [4]{b x^3+a x^4}}{96 a^3}-\frac {155 b^3 \tan ^{-1}\left (\frac {\sqrt [4]{a} x}{\sqrt [4]{b x^3+a x^4}}\right )}{64 a^{15/4}}+\frac {2 \sqrt [4]{2} b^3 \tan ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} x}{\sqrt [4]{b x^3+a x^4}}\right )}{a^{15/4}}+\frac {155 b^3 \tanh ^{-1}\left (\frac {\sqrt [4]{a} x}{\sqrt [4]{b x^3+a x^4}}\right )}{64 a^{15/4}}-\frac {2 \sqrt [4]{2} b^3 \tanh ^{-1}\left (\frac {\sqrt [4]{2} \sqrt [4]{a} x}{\sqrt [4]{b x^3+a x^4}}\right )}{a^{15/4}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.50, size = 489, normalized size = 2.47 \begin {gather*} \frac {1536 \cdot 2^{\frac {1}{4}} a^{3} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} \arctan \left (-\frac {2^{\frac {3}{4}} {\left (a x^{4} + b x^{3}\right )}^{\frac {1}{4}} a^{11} b^{3} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {3}{4}} - 2^{\frac {3}{4}} a^{11} x \sqrt {\frac {\sqrt {2} a^{8} x^{2} \sqrt {\frac {b^{12}}{a^{15}}} + \sqrt {a x^{4} + b x^{3}} b^{6}}{x^{2}}} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {3}{4}}}{2 \, b^{12} x}\right ) - 384 \cdot 2^{\frac {1}{4}} a^{3} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} \log \left (\frac {2^{\frac {1}{4}} a^{4} x \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} + {\left (a x^{4} + b x^{3}\right )}^{\frac {1}{4}} b^{3}}{x}\right ) + 384 \cdot 2^{\frac {1}{4}} a^{3} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} \log \left (-\frac {2^{\frac {1}{4}} a^{4} x \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} - {\left (a x^{4} + b x^{3}\right )}^{\frac {1}{4}} b^{3}}{x}\right ) - 1860 \, a^{3} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} \arctan \left (-\frac {{\left (a x^{4} + b x^{3}\right )}^{\frac {1}{4}} a^{11} b^{3} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {3}{4}} - a^{11} x \sqrt {\frac {a^{8} x^{2} \sqrt {\frac {b^{12}}{a^{15}}} + \sqrt {a x^{4} + b x^{3}} b^{6}}{x^{2}}} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {3}{4}}}{b^{12} x}\right ) + 465 \, a^{3} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} \log \left (\frac {155 \, {\left (a^{4} x \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} + {\left (a x^{4} + b x^{3}\right )}^{\frac {1}{4}} b^{3}\right )}}{x}\right ) - 465 \, a^{3} \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} \log \left (-\frac {155 \, {\left (a^{4} x \left (\frac {b^{12}}{a^{15}}\right )^{\frac {1}{4}} - {\left (a x^{4} + b x^{3}\right )}^{\frac {1}{4}} b^{3}\right )}}{x}\right ) + 4 \, {\left (a x^{4} + b x^{3}\right )}^{\frac {1}{4}} {\left (32 \, a^{2} x^{2} + 52 \, a b x + 101 \, b^{2}\right )}}{384 \, a^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.86, size = 461, normalized size = 2.33 \begin {gather*} -\frac {2^{\frac {3}{4}} \left (-a\right )^{\frac {1}{4}} b^{3} \arctan \left (\frac {2^{\frac {1}{4}} {\left (2^{\frac {3}{4}} \left (-a\right )^{\frac {1}{4}} + 2 \, {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}}\right )}}{2 \, \left (-a\right )^{\frac {1}{4}}}\right )}{a^{4}} - \frac {2^{\frac {3}{4}} \left (-a\right )^{\frac {1}{4}} b^{3} \arctan \left (-\frac {2^{\frac {1}{4}} {\left (2^{\frac {3}{4}} \left (-a\right )^{\frac {1}{4}} - 2 \, {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}}\right )}}{2 \, \left (-a\right )^{\frac {1}{4}}}\right )}{a^{4}} - \frac {2^{\frac {3}{4}} \left (-a\right )^{\frac {1}{4}} b^{3} \log \left (2^{\frac {3}{4}} \left (-a\right )^{\frac {1}{4}} {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}} + \sqrt {2} \sqrt {-a} + \sqrt {a + \frac {b}{x}}\right )}{2 \, a^{4}} + \frac {2^{\frac {3}{4}} \left (-a\right )^{\frac {1}{4}} b^{3} \log \left (-2^{\frac {3}{4}} \left (-a\right )^{\frac {1}{4}} {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}} + \sqrt {2} \sqrt {-a} + \sqrt {a + \frac {b}{x}}\right )}{2 \, a^{4}} + \frac {155 \, \sqrt {2} \left (-a\right )^{\frac {1}{4}} b^{3} \arctan \left (\frac {\sqrt {2} {\left (\sqrt {2} \left (-a\right )^{\frac {1}{4}} + 2 \, {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}}\right )}}{2 \, \left (-a\right )^{\frac {1}{4}}}\right )}{128 \, a^{4}} + \frac {155 \, \sqrt {2} \left (-a\right )^{\frac {1}{4}} b^{3} \arctan \left (-\frac {\sqrt {2} {\left (\sqrt {2} \left (-a\right )^{\frac {1}{4}} - 2 \, {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}}\right )}}{2 \, \left (-a\right )^{\frac {1}{4}}}\right )}{128 \, a^{4}} + \frac {155 \, \sqrt {2} \left (-a\right )^{\frac {1}{4}} b^{3} \log \left (\sqrt {2} \left (-a\right )^{\frac {1}{4}} {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}} + \sqrt {-a} + \sqrt {a + \frac {b}{x}}\right )}{256 \, a^{4}} + \frac {155 \, \sqrt {2} b^{3} \log \left (-\sqrt {2} \left (-a\right )^{\frac {1}{4}} {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}} + \sqrt {-a} + \sqrt {a + \frac {b}{x}}\right )}{256 \, \left (-a\right )^{\frac {3}{4}} a^{3}} + \frac {{\left (101 \, {\left (a + \frac {b}{x}\right )}^{\frac {9}{4}} b^{3} - 150 \, {\left (a + \frac {b}{x}\right )}^{\frac {5}{4}} a b^{3} + 81 \, {\left (a + \frac {b}{x}\right )}^{\frac {1}{4}} a^{2} b^{3}\right )} x^{3}}{96 \, a^{3} b^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {x^{2} \left (a \,x^{4}+b \,x^{3}\right )^{\frac {1}{4}}}{a x -b}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (a x^{4} + b x^{3}\right )}^{\frac {1}{4}} x^{2}}{a x - b}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} -\int \frac {x^2\,{\left (a\,x^4+b\,x^3\right )}^{1/4}}{b-a\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{2} \sqrt [4]{x^{3} \left (a x + b\right )}}{a x - b}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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