Optimal. Leaf size=62 \[ -\frac{a^2 \left (a-b x^4\right )^{3/4}}{3 b^3}-\frac{\left (a-b x^4\right )^{11/4}}{11 b^3}+\frac{2 a \left (a-b x^4\right )^{7/4}}{7 b^3} \]
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Rubi [A] time = 0.0337152, antiderivative size = 62, normalized size of antiderivative = 1., 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 = {266, 43} \[ -\frac{a^2 \left (a-b x^4\right )^{3/4}}{3 b^3}-\frac{\left (a-b x^4\right )^{11/4}}{11 b^3}+\frac{2 a \left (a-b x^4\right )^{7/4}}{7 b^3} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{11}}{\sqrt [4]{a-b x^4}} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \frac{x^2}{\sqrt [4]{a-b x}} \, dx,x,x^4\right )\\ &=\frac{1}{4} \operatorname{Subst}\left (\int \left (\frac{a^2}{b^2 \sqrt [4]{a-b x}}-\frac{2 a (a-b x)^{3/4}}{b^2}+\frac{(a-b x)^{7/4}}{b^2}\right ) \, dx,x,x^4\right )\\ &=-\frac{a^2 \left (a-b x^4\right )^{3/4}}{3 b^3}+\frac{2 a \left (a-b x^4\right )^{7/4}}{7 b^3}-\frac{\left (a-b x^4\right )^{11/4}}{11 b^3}\\ \end{align*}
Mathematica [A] time = 0.0185193, size = 40, normalized size = 0.65 \[ -\frac{\left (a-b x^4\right )^{3/4} \left (32 a^2+24 a b x^4+21 b^2 x^8\right )}{231 b^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 37, normalized size = 0.6 \begin{align*} -{\frac{21\,{b}^{2}{x}^{8}+24\,ab{x}^{4}+32\,{a}^{2}}{231\,{b}^{3}} \left ( -b{x}^{4}+a \right ) ^{{\frac{3}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.982893, size = 68, normalized size = 1.1 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{11}{4}}}{11 \, b^{3}} + \frac{2 \,{\left (-b x^{4} + a\right )}^{\frac{7}{4}} a}{7 \, b^{3}} - \frac{{\left (-b x^{4} + a\right )}^{\frac{3}{4}} a^{2}}{3 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49944, size = 89, normalized size = 1.44 \begin{align*} -\frac{{\left (21 \, b^{2} x^{8} + 24 \, a b x^{4} + 32 \, a^{2}\right )}{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}{231 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.3967, size = 70, normalized size = 1.13 \begin{align*} \begin{cases} - \frac{32 a^{2} \left (a - b x^{4}\right )^{\frac{3}{4}}}{231 b^{3}} - \frac{8 a x^{4} \left (a - b x^{4}\right )^{\frac{3}{4}}}{77 b^{2}} - \frac{x^{8} \left (a - b x^{4}\right )^{\frac{3}{4}}}{11 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 \sqrt [4]{a}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16955, size = 77, normalized size = 1.24 \begin{align*} -\frac{21 \,{\left (b x^{4} - a\right )}^{2}{\left (-b x^{4} + a\right )}^{\frac{3}{4}} - 66 \,{\left (-b x^{4} + a\right )}^{\frac{7}{4}} a + 77 \,{\left (-b x^{4} + a\right )}^{\frac{3}{4}} a^{2}}{231 \, b^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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