Optimal. Leaf size=71 \[ -\frac {32 b^2 \sqrt [4]{a-b x^4}}{45 a^3 x}-\frac {8 b \sqrt [4]{a-b x^4}}{45 a^2 x^5}-\frac {\sqrt [4]{a-b x^4}}{9 a x^9} \]
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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} \[ -\frac {32 b^2 \sqrt [4]{a-b x^4}}{45 a^3 x}-\frac {8 b \sqrt [4]{a-b x^4}}{45 a^2 x^5}-\frac {\sqrt [4]{a-b x^4}}{9 a x^9} \]
Antiderivative was successfully verified.
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Rule 264
Rule 271
Rubi steps
\begin {align*} \int \frac {1}{x^{10} \left (a-b x^4\right )^{3/4}} \, dx &=-\frac {\sqrt [4]{a-b x^4}}{9 a x^9}+\frac {(8 b) \int \frac {1}{x^6 \left (a-b x^4\right )^{3/4}} \, dx}{9 a}\\ &=-\frac {\sqrt [4]{a-b x^4}}{9 a x^9}-\frac {8 b \sqrt [4]{a-b x^4}}{45 a^2 x^5}+\frac {\left (32 b^2\right ) \int \frac {1}{x^2 \left (a-b x^4\right )^{3/4}} \, dx}{45 a^2}\\ &=-\frac {\sqrt [4]{a-b x^4}}{9 a x^9}-\frac {8 b \sqrt [4]{a-b x^4}}{45 a^2 x^5}-\frac {32 b^2 \sqrt [4]{a-b x^4}}{45 a^3 x}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 43, normalized size = 0.61 \[ -\frac {\sqrt [4]{a-b x^4} \left (5 a^2+8 a b x^4+32 b^2 x^8\right )}{45 a^3 x^9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 39, normalized size = 0.55 \[ -\frac {{\left (32 \, b^{2} x^{8} + 8 \, a b x^{4} + 5 \, a^{2}\right )} {\left (-b x^{4} + a\right )}^{\frac {1}{4}}}{45 \, a^{3} x^{9}} \]
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 \[ \int \frac {1}{{\left (-b x^{4} + a\right )}^{\frac {3}{4}} x^{10}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.56 \[ -\frac {\left (-b \,x^{4}+a \right )^{\frac {1}{4}} \left (32 b^{2} x^{8}+8 a b \,x^{4}+5 a^{2}\right )}{45 a^{3} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.11, size = 55, normalized size = 0.77 \[ -\frac {\frac {45 \, {\left (-b x^{4} + a\right )}^{\frac {1}{4}} b^{2}}{x} + \frac {18 \, {\left (-b x^{4} + a\right )}^{\frac {5}{4}} b}{x^{5}} + \frac {5 \, {\left (-b x^{4} + a\right )}^{\frac {9}{4}}}{x^{9}}}{45 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.29, size = 39, normalized size = 0.55 \[ -\frac {{\left (a-b\,x^4\right )}^{1/4}\,\left (5\,a^2+8\,a\,b\,x^4+32\,b^2\,x^8\right )}{45\,a^3\,x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 2.36, size = 1110, normalized size = 15.63 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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