Optimal. Leaf size=116 \[ -\frac{2048 b^4 \left (a+b x^4\right )^{3/4}}{21945 a^5 x^3}+\frac{512 b^3 \left (a+b x^4\right )^{3/4}}{7315 a^4 x^7}-\frac{64 b^2 \left (a+b x^4\right )^{3/4}}{1045 a^3 x^{11}}+\frac{16 b \left (a+b x^4\right )^{3/4}}{285 a^2 x^{15}}-\frac{\left (a+b x^4\right )^{3/4}}{19 a x^{19}} \]
[Out]
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Rubi [A] time = 0.121524, antiderivative size = 116, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{2048 b^4 \left (a+b x^4\right )^{3/4}}{21945 a^5 x^3}+\frac{512 b^3 \left (a+b x^4\right )^{3/4}}{7315 a^4 x^7}-\frac{64 b^2 \left (a+b x^4\right )^{3/4}}{1045 a^3 x^{11}}+\frac{16 b \left (a+b x^4\right )^{3/4}}{285 a^2 x^{15}}-\frac{\left (a+b x^4\right )^{3/4}}{19 a x^{19}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^20*(a + b*x^4)^(1/4)),x]
[Out]
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Rubi in Sympy [A] time = 13.5241, size = 109, normalized size = 0.94 \[ - \frac{\left (a + b x^{4}\right )^{\frac{3}{4}}}{19 a x^{19}} + \frac{16 b \left (a + b x^{4}\right )^{\frac{3}{4}}}{285 a^{2} x^{15}} - \frac{64 b^{2} \left (a + b x^{4}\right )^{\frac{3}{4}}}{1045 a^{3} x^{11}} + \frac{512 b^{3} \left (a + b x^{4}\right )^{\frac{3}{4}}}{7315 a^{4} x^{7}} - \frac{2048 b^{4} \left (a + b x^{4}\right )^{\frac{3}{4}}}{21945 a^{5} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**20/(b*x**4+a)**(1/4),x)
[Out]
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Mathematica [A] time = 0.0482928, size = 64, normalized size = 0.55 \[ -\frac{\left (a+b x^4\right )^{3/4} \left (1155 a^4-1232 a^3 b x^4+1344 a^2 b^2 x^8-1536 a b^3 x^{12}+2048 b^4 x^{16}\right )}{21945 a^5 x^{19}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^20*(a + b*x^4)^(1/4)),x]
[Out]
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Maple [A] time = 0.011, size = 61, normalized size = 0.5 \[ -{\frac{2048\,{x}^{16}{b}^{4}-1536\,a{x}^{12}{b}^{3}+1344\,{a}^{2}{x}^{8}{b}^{2}-1232\,{a}^{3}{x}^{4}b+1155\,{a}^{4}}{21945\,{x}^{19}{a}^{5}} \left ( b{x}^{4}+a \right ) ^{{\frac{3}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^20/(b*x^4+a)^(1/4),x)
[Out]
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Maxima [A] time = 1.42251, size = 116, normalized size = 1. \[ -\frac{\frac{7315 \,{\left (b x^{4} + a\right )}^{\frac{3}{4}} b^{4}}{x^{3}} - \frac{12540 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} b^{3}}{x^{7}} + \frac{11970 \,{\left (b x^{4} + a\right )}^{\frac{11}{4}} b^{2}}{x^{11}} - \frac{5852 \,{\left (b x^{4} + a\right )}^{\frac{15}{4}} b}{x^{15}} + \frac{1155 \,{\left (b x^{4} + a\right )}^{\frac{19}{4}}}{x^{19}}}{21945 \, a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(1/4)*x^20),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248188, size = 81, normalized size = 0.7 \[ -\frac{{\left (2048 \, b^{4} x^{16} - 1536 \, a b^{3} x^{12} + 1344 \, a^{2} b^{2} x^{8} - 1232 \, a^{3} b x^{4} + 1155 \, a^{4}\right )}{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{21945 \, a^{5} x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(1/4)*x^20),x, algorithm="fricas")
[Out]
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Sympy [A] time = 40.2115, size = 1046, normalized size = 9.02 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**20/(b*x**4+a)**(1/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{1}{4}} x^{20}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(1/4)*x^20),x, algorithm="giac")
[Out]