Optimal. Leaf size=71 \[ -\frac {32 b^2 \left (a-b x^4\right )^{5/4}}{585 a^3 x^5}-\frac {8 b \left (a-b x^4\right )^{5/4}}{117 a^2 x^9}-\frac {\left (a-b x^4\right )^{5/4}}{13 a x^{13}} \]
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Rubi [A] time = 0.02, antiderivative size = 71, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {271, 264} \[ -\frac {32 b^2 \left (a-b x^4\right )^{5/4}}{585 a^3 x^5}-\frac {8 b \left (a-b x^4\right )^{5/4}}{117 a^2 x^9}-\frac {\left (a-b x^4\right )^{5/4}}{13 a x^{13}} \]
Antiderivative was successfully verified.
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Rule 264
Rule 271
Rubi steps
\begin {align*} \int \frac {\sqrt [4]{a-b x^4}}{x^{14}} \, dx &=-\frac {\left (a-b x^4\right )^{5/4}}{13 a x^{13}}+\frac {(8 b) \int \frac {\sqrt [4]{a-b x^4}}{x^{10}} \, dx}{13 a}\\ &=-\frac {\left (a-b x^4\right )^{5/4}}{13 a x^{13}}-\frac {8 b \left (a-b x^4\right )^{5/4}}{117 a^2 x^9}+\frac {\left (32 b^2\right ) \int \frac {\sqrt [4]{a-b x^4}}{x^6} \, dx}{117 a^2}\\ &=-\frac {\left (a-b x^4\right )^{5/4}}{13 a x^{13}}-\frac {8 b \left (a-b x^4\right )^{5/4}}{117 a^2 x^9}-\frac {32 b^2 \left (a-b x^4\right )^{5/4}}{585 a^3 x^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 43, normalized size = 0.61 \[ -\frac {\left (a-b x^4\right )^{5/4} \left (45 a^2+40 a b x^4+32 b^2 x^8\right )}{585 a^3 x^{13}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 50, normalized size = 0.70 \[ \frac {{\left (32 \, b^{3} x^{12} + 8 \, a b^{2} x^{8} + 5 \, a^{2} b x^{4} - 45 \, a^{3}\right )} {\left (-b x^{4} + a\right )}^{\frac {1}{4}}}{585 \, a^{3} x^{13}} \]
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 \[ \int \frac {{\left (-b x^{4} + a\right )}^{\frac {1}{4}}}{x^{14}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 40, normalized size = 0.56 \[ -\frac {\left (-b \,x^{4}+a \right )^{\frac {5}{4}} \left (32 b^{2} x^{8}+40 a b \,x^{4}+45 a^{2}\right )}{585 a^{3} x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.42, size = 55, normalized size = 0.77 \[ -\frac {\frac {117 \, {\left (-b x^{4} + a\right )}^{\frac {5}{4}} b^{2}}{x^{5}} + \frac {130 \, {\left (-b x^{4} + a\right )}^{\frac {9}{4}} b}{x^{9}} + \frac {45 \, {\left (-b x^{4} + a\right )}^{\frac {13}{4}}}{x^{13}}}{585 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.48, size = 77, normalized size = 1.08 \[ \frac {b\,{\left (a-b\,x^4\right )}^{1/4}}{117\,a\,x^9}-\frac {{\left (a-b\,x^4\right )}^{1/4}}{13\,x^{13}}+\frac {32\,b^3\,{\left (a-b\,x^4\right )}^{1/4}}{585\,a^3\,x}+\frac {8\,b^2\,{\left (a-b\,x^4\right )}^{1/4}}{585\,a^2\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 4.23, size = 1090, normalized size = 15.35 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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