Optimal. Leaf size=21 \[ -\frac{\left (a+b x^4\right )^{7/4}}{7 a x^7} \]
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Rubi [A] time = 0.0044587, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {264} \[ -\frac{\left (a+b x^4\right )^{7/4}}{7 a x^7} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^4\right )^{3/4}}{x^8} \, dx &=-\frac{\left (a+b x^4\right )^{7/4}}{7 a x^7}\\ \end{align*}
Mathematica [A] time = 0.0051894, size = 21, normalized size = 1. \[ -\frac{\left (a+b x^4\right )^{7/4}}{7 a x^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 18, normalized size = 0.9 \begin{align*} -{\frac{1}{7\,a{x}^{7}} \left ( b{x}^{4}+a \right ) ^{{\frac{7}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.980219, size = 23, normalized size = 1.1 \begin{align*} -\frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, a x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73672, size = 43, normalized size = 2.05 \begin{align*} -\frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, a x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.05122, size = 68, normalized size = 3.24 \begin{align*} \frac{b^{\frac{3}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{7}{4}\right )}{4 x^{4} \Gamma \left (- \frac{3}{4}\right )} + \frac{b^{\frac{7}{4}} \left (\frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{7}{4}\right )}{4 a \Gamma \left (- \frac{3}{4}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{x^{8}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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