Optimal. Leaf size=92 \[ \frac{128 b^3 \sqrt [4]{a+b x^4}}{195 a^4 x}-\frac{32 b^2 \sqrt [4]{a+b x^4}}{195 a^3 x^5}+\frac{4 b \sqrt [4]{a+b x^4}}{39 a^2 x^9}-\frac{\sqrt [4]{a+b x^4}}{13 a x^{13}} \]
[Out]
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Rubi [A] time = 0.0891185, 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 \[ \frac{128 b^3 \sqrt [4]{a+b x^4}}{195 a^4 x}-\frac{32 b^2 \sqrt [4]{a+b x^4}}{195 a^3 x^5}+\frac{4 b \sqrt [4]{a+b x^4}}{39 a^2 x^9}-\frac{\sqrt [4]{a+b x^4}}{13 a x^{13}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^14*(a + b*x^4)^(3/4)),x]
[Out]
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Rubi in Sympy [A] time = 9.71617, size = 83, normalized size = 0.9 \[ - \frac{\sqrt [4]{a + b x^{4}}}{13 a x^{13}} + \frac{4 b \sqrt [4]{a + b x^{4}}}{39 a^{2} x^{9}} - \frac{32 b^{2} \sqrt [4]{a + b x^{4}}}{195 a^{3} x^{5}} + \frac{128 b^{3} \sqrt [4]{a + b x^{4}}}{195 a^{4} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**14/(b*x**4+a)**(3/4),x)
[Out]
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Mathematica [A] time = 0.0418656, size = 53, normalized size = 0.58 \[ \frac{\sqrt [4]{a+b x^4} \left (-15 a^3+20 a^2 b x^4-32 a b^2 x^8+128 b^3 x^{12}\right )}{195 a^4 x^{13}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^14*(a + b*x^4)^(3/4)),x]
[Out]
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Maple [A] time = 0.009, size = 50, normalized size = 0.5 \[ -{\frac{-128\,{b}^{3}{x}^{12}+32\,a{b}^{2}{x}^{8}-20\,{a}^{2}b{x}^{4}+15\,{a}^{3}}{195\,{x}^{13}{a}^{4}}\sqrt [4]{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^14/(b*x^4+a)^(3/4),x)
[Out]
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Maxima [A] time = 1.43968, size = 93, normalized size = 1.01 \[ \frac{\frac{195 \,{\left (b x^{4} + a\right )}^{\frac{1}{4}} b^{3}}{x} - \frac{117 \,{\left (b x^{4} + a\right )}^{\frac{5}{4}} b^{2}}{x^{5}} + \frac{65 \,{\left (b x^{4} + a\right )}^{\frac{9}{4}} b}{x^{9}} - \frac{15 \,{\left (b x^{4} + a\right )}^{\frac{13}{4}}}{x^{13}}}{195 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(3/4)*x^14),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.241879, size = 66, normalized size = 0.72 \[ \frac{{\left (128 \, b^{3} x^{12} - 32 \, a b^{2} x^{8} + 20 \, a^{2} b x^{4} - 15 \, a^{3}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{195 \, a^{4} x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(3/4)*x^14),x, algorithm="fricas")
[Out]
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Sympy [A] time = 22.7152, size = 692, normalized size = 7.52 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**14/(b*x**4+a)**(3/4),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{3}{4}} x^{14}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^4 + a)^(3/4)*x^14),x, algorithm="giac")
[Out]