Optimal. Leaf size=92 \[ \frac{128 b^3 \left (a+b x^4\right )^{7/4}}{7315 a^4 x^7}-\frac{32 b^2 \left (a+b x^4\right )^{7/4}}{1045 a^3 x^{11}}+\frac{4 b \left (a+b x^4\right )^{7/4}}{95 a^2 x^{15}}-\frac{\left (a+b x^4\right )^{7/4}}{19 a x^{19}} \]
[Out]
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Rubi [A] time = 0.0904368, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{128 b^3 \left (a+b x^4\right )^{7/4}}{7315 a^4 x^7}-\frac{32 b^2 \left (a+b x^4\right )^{7/4}}{1045 a^3 x^{11}}+\frac{4 b \left (a+b x^4\right )^{7/4}}{95 a^2 x^{15}}-\frac{\left (a+b x^4\right )^{7/4}}{19 a x^{19}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^4)^(3/4)/x^20,x]
[Out]
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Rubi in Sympy [A] time = 9.77648, size = 85, normalized size = 0.92 \[ - \frac{\left (a + b x^{4}\right )^{\frac{7}{4}}}{19 a x^{19}} + \frac{4 b \left (a + b x^{4}\right )^{\frac{7}{4}}}{95 a^{2} x^{15}} - \frac{32 b^{2} \left (a + b x^{4}\right )^{\frac{7}{4}}}{1045 a^{3} x^{11}} + \frac{128 b^{3} \left (a + b x^{4}\right )^{\frac{7}{4}}}{7315 a^{4} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**4+a)**(3/4)/x**20,x)
[Out]
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Mathematica [A] time = 0.0401515, size = 64, normalized size = 0.7 \[ -\frac{\left (a+b x^4\right )^{3/4} \left (385 a^4+77 a^3 b x^4-84 a^2 b^2 x^8+96 a b^3 x^{12}-128 b^4 x^{16}\right )}{7315 a^4 x^{19}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^4)^(3/4)/x^20,x]
[Out]
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Maple [A] time = 0.01, size = 50, normalized size = 0.5 \[ -{\frac{-128\,{b}^{3}{x}^{12}+224\,a{b}^{2}{x}^{8}-308\,{a}^{2}b{x}^{4}+385\,{a}^{3}}{7315\,{x}^{19}{a}^{4}} \left ( b{x}^{4}+a \right ) ^{{\frac{7}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^4+a)^(3/4)/x^20,x)
[Out]
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Maxima [A] time = 1.43583, size = 93, normalized size = 1.01 \[ \frac{\frac{1045 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} b^{3}}{x^{7}} - \frac{1995 \,{\left (b x^{4} + a\right )}^{\frac{11}{4}} b^{2}}{x^{11}} + \frac{1463 \,{\left (b x^{4} + a\right )}^{\frac{15}{4}} b}{x^{15}} - \frac{385 \,{\left (b x^{4} + a\right )}^{\frac{19}{4}}}{x^{19}}}{7315 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^20,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.32024, size = 81, normalized size = 0.88 \[ \frac{{\left (128 \, b^{4} x^{16} - 96 \, a b^{3} x^{12} + 84 \, a^{2} b^{2} x^{8} - 77 \, a^{3} b x^{4} - 385 \, a^{4}\right )}{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{7315 \, a^{4} x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^20,x, algorithm="fricas")
[Out]
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Sympy [A] time = 65.7367, size = 847, normalized size = 9.21 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**4+a)**(3/4)/x**20,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{x^{20}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^4 + a)^(3/4)/x^20,x, algorithm="giac")
[Out]