Optimal. Leaf size=44 \[ -\frac {\left (a+b x^4\right )^{5/4}}{9 a x^9}+\frac {4 b \left (a+b x^4\right )^{5/4}}{45 a^2 x^5} \]
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Rubi [A]
time = 0.01, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {277, 270}
\begin {gather*} \frac {4 b \left (a+b x^4\right )^{5/4}}{45 a^2 x^5}-\frac {\left (a+b x^4\right )^{5/4}}{9 a x^9} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rule 277
Rubi steps
\begin {align*} \int \frac {\sqrt [4]{a+b x^4}}{x^{10}} \, dx &=-\frac {\left (a+b x^4\right )^{5/4}}{9 a x^9}-\frac {(4 b) \int \frac {\sqrt [4]{a+b x^4}}{x^6} \, dx}{9 a}\\ &=-\frac {\left (a+b x^4\right )^{5/4}}{9 a x^9}+\frac {4 b \left (a+b x^4\right )^{5/4}}{45 a^2 x^5}\\ \end {align*}
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Mathematica [A]
time = 0.12, size = 42, normalized size = 0.95 \begin {gather*} \frac {\sqrt [4]{a+b x^4} \left (-5 a^2-a b x^4+4 b^2 x^8\right )}{45 a^2 x^9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 28, normalized size = 0.64
method | result | size |
gosper | \(-\frac {\left (b \,x^{4}+a \right )^{\frac {5}{4}} \left (-4 b \,x^{4}+5 a \right )}{45 a^{2} x^{9}}\) | \(28\) |
trager | \(-\frac {\left (-4 b^{2} x^{8}+a b \,x^{4}+5 a^{2}\right ) \left (b \,x^{4}+a \right )^{\frac {1}{4}}}{45 a^{2} x^{9}}\) | \(38\) |
risch | \(-\frac {\left (-4 b^{2} x^{8}+a b \,x^{4}+5 a^{2}\right ) \left (b \,x^{4}+a \right )^{\frac {1}{4}}}{45 a^{2} x^{9}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 35, normalized size = 0.80 \begin {gather*} \frac {\frac {9 \, {\left (b x^{4} + a\right )}^{\frac {5}{4}} b}{x^{5}} - \frac {5 \, {\left (b x^{4} + a\right )}^{\frac {9}{4}}}{x^{9}}}{45 \, a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 38, normalized size = 0.86 \begin {gather*} \frac {{\left (4 \, b^{2} x^{8} - a b x^{4} - 5 \, a^{2}\right )} {\left (b x^{4} + a\right )}^{\frac {1}{4}}}{45 \, a^{2} x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 109 vs.
\(2 (37) = 74\).
time = 0.65, size = 109, normalized size = 2.48 \begin {gather*} - \frac {5 \sqrt [4]{b} \sqrt [4]{\frac {a}{b x^{4}} + 1} \Gamma \left (- \frac {9}{4}\right )}{16 x^{8} \Gamma \left (- \frac {1}{4}\right )} - \frac {b^{\frac {5}{4}} \sqrt [4]{\frac {a}{b x^{4}} + 1} \Gamma \left (- \frac {9}{4}\right )}{16 a x^{4} \Gamma \left (- \frac {1}{4}\right )} + \frac {b^{\frac {9}{4}} \sqrt [4]{\frac {a}{b x^{4}} + 1} \Gamma \left (- \frac {9}{4}\right )}{4 a^{2} \Gamma \left (- \frac {1}{4}\right )} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.30, size = 37, normalized size = 0.84 \begin {gather*} -\frac {{\left (b\,x^4+a\right )}^{1/4}\,\left (5\,a^2+a\,b\,x^4-4\,b^2\,x^8\right )}{45\,a^2\,x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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