Optimal. Leaf size=130 \[ -\frac {b^{5/2} \left (1-\frac {b x^4}{a}\right )^{3/4} F\left (\left .\frac {1}{2} \sin ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )\right |2\right )}{24 a^{3/2} \left (a-b x^4\right )^{3/4}}+\frac {b^2 \sqrt [4]{a-b x^4}}{24 a^2 x^2}-\frac {\sqrt [4]{a-b x^4}}{10 x^{10}}+\frac {b \sqrt [4]{a-b x^4}}{60 a x^6} \]
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Rubi [A] time = 0.09, antiderivative size = 130, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.312, Rules used = {275, 277, 325, 233, 232} \[ \frac {b^2 \sqrt [4]{a-b x^4}}{24 a^2 x^2}-\frac {b^{5/2} \left (1-\frac {b x^4}{a}\right )^{3/4} F\left (\left .\frac {1}{2} \sin ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )\right |2\right )}{24 a^{3/2} \left (a-b x^4\right )^{3/4}}+\frac {b \sqrt [4]{a-b x^4}}{60 a x^6}-\frac {\sqrt [4]{a-b x^4}}{10 x^{10}} \]
Antiderivative was successfully verified.
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Rule 232
Rule 233
Rule 275
Rule 277
Rule 325
Rubi steps
\begin {align*} \int \frac {\sqrt [4]{a-b x^4}}{x^{11}} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {\sqrt [4]{a-b x^2}}{x^6} \, dx,x,x^2\right )\\ &=-\frac {\sqrt [4]{a-b x^4}}{10 x^{10}}-\frac {1}{20} b \operatorname {Subst}\left (\int \frac {1}{x^4 \left (a-b x^2\right )^{3/4}} \, dx,x,x^2\right )\\ &=-\frac {\sqrt [4]{a-b x^4}}{10 x^{10}}+\frac {b \sqrt [4]{a-b x^4}}{60 a x^6}-\frac {b^2 \operatorname {Subst}\left (\int \frac {1}{x^2 \left (a-b x^2\right )^{3/4}} \, dx,x,x^2\right )}{24 a}\\ &=-\frac {\sqrt [4]{a-b x^4}}{10 x^{10}}+\frac {b \sqrt [4]{a-b x^4}}{60 a x^6}+\frac {b^2 \sqrt [4]{a-b x^4}}{24 a^2 x^2}-\frac {b^3 \operatorname {Subst}\left (\int \frac {1}{\left (a-b x^2\right )^{3/4}} \, dx,x,x^2\right )}{48 a^2}\\ &=-\frac {\sqrt [4]{a-b x^4}}{10 x^{10}}+\frac {b \sqrt [4]{a-b x^4}}{60 a x^6}+\frac {b^2 \sqrt [4]{a-b x^4}}{24 a^2 x^2}-\frac {\left (b^3 \left (1-\frac {b x^4}{a}\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {1}{\left (1-\frac {b x^2}{a}\right )^{3/4}} \, dx,x,x^2\right )}{48 a^2 \left (a-b x^4\right )^{3/4}}\\ &=-\frac {\sqrt [4]{a-b x^4}}{10 x^{10}}+\frac {b \sqrt [4]{a-b x^4}}{60 a x^6}+\frac {b^2 \sqrt [4]{a-b x^4}}{24 a^2 x^2}-\frac {b^{5/2} \left (1-\frac {b x^4}{a}\right )^{3/4} F\left (\left .\frac {1}{2} \sin ^{-1}\left (\frac {\sqrt {b} x^2}{\sqrt {a}}\right )\right |2\right )}{24 a^{3/2} \left (a-b x^4\right )^{3/4}}\\ \end {align*}
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Mathematica [C] time = 0.03, size = 52, normalized size = 0.40 \[ -\frac {\sqrt [4]{a-b x^4} \, _2F_1\left (-\frac {5}{2},-\frac {1}{4};-\frac {3}{2};\frac {b x^4}{a}\right )}{10 x^{10} \sqrt [4]{1-\frac {b x^4}{a}}} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.79, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (-b x^{4} + a\right )}^{\frac {1}{4}}}{x^{11}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (-b x^{4} + a\right )}^{\frac {1}{4}}}{x^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {\left (-b \,x^{4}+a \right )^{\frac {1}{4}}}{x^{11}}\, dx \]
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 \[ \int \frac {{\left (-b x^{4} + a\right )}^{\frac {1}{4}}}{x^{11}}\,{d x} \]
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 \[ \int \frac {{\left (a-b\,x^4\right )}^{1/4}}{x^{11}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 2.39, size = 36, normalized size = 0.28 \[ - \frac {\sqrt [4]{a} {{}_{2}F_{1}\left (\begin {matrix} - \frac {5}{2}, - \frac {1}{4} \\ - \frac {3}{2} \end {matrix}\middle | {\frac {b x^{4} e^{2 i \pi }}{a}} \right )}}{10 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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