Optimal. Leaf size=78 \[ -\frac{a^3 \sqrt [4]{a+b x^4}}{b^4}+\frac{3 a^2 \left (a+b x^4\right )^{5/4}}{5 b^4}+\frac{\left (a+b x^4\right )^{13/4}}{13 b^4}-\frac{a \left (a+b x^4\right )^{9/4}}{3 b^4} \]
[Out]
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Rubi [A] time = 0.107357, antiderivative size = 78, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{a^3 \sqrt [4]{a+b x^4}}{b^4}+\frac{3 a^2 \left (a+b x^4\right )^{5/4}}{5 b^4}+\frac{\left (a+b x^4\right )^{13/4}}{13 b^4}-\frac{a \left (a+b x^4\right )^{9/4}}{3 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^15/(a + b*x^4)^(3/4),x]
[Out]
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Rubi in Sympy [A] time = 14.1173, size = 68, normalized size = 0.87 \[ - \frac{a^{3} \sqrt [4]{a + b x^{4}}}{b^{4}} + \frac{3 a^{2} \left (a + b x^{4}\right )^{\frac{5}{4}}}{5 b^{4}} - \frac{a \left (a + b x^{4}\right )^{\frac{9}{4}}}{3 b^{4}} + \frac{\left (a + b x^{4}\right )^{\frac{13}{4}}}{13 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**15/(b*x**4+a)**(3/4),x)
[Out]
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Mathematica [A] time = 0.0310291, size = 50, normalized size = 0.64 \[ \frac{\sqrt [4]{a+b x^4} \left (-128 a^3+32 a^2 b x^4-20 a b^2 x^8+15 b^3 x^{12}\right )}{195 b^4} \]
Antiderivative was successfully verified.
[In] Integrate[x^15/(a + b*x^4)^(3/4),x]
[Out]
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Maple [A] time = 0.009, size = 47, normalized size = 0.6 \[ -{\frac{-15\,{b}^{3}{x}^{12}+20\,a{b}^{2}{x}^{8}-32\,{a}^{2}b{x}^{4}+128\,{a}^{3}}{195\,{b}^{4}}\sqrt [4]{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^15/(b*x^4+a)^(3/4),x)
[Out]
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Maxima [A] time = 1.43708, size = 86, normalized size = 1.1 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{13}{4}}}{13 \, b^{4}} - \frac{{\left (b x^{4} + a\right )}^{\frac{9}{4}} a}{3 \, b^{4}} + \frac{3 \,{\left (b x^{4} + a\right )}^{\frac{5}{4}} a^{2}}{5 \, b^{4}} - \frac{{\left (b x^{4} + a\right )}^{\frac{1}{4}} a^{3}}{b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^15/(b*x^4 + a)^(3/4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232329, size = 62, normalized size = 0.79 \[ \frac{{\left (15 \, b^{3} x^{12} - 20 \, a b^{2} x^{8} + 32 \, a^{2} b x^{4} - 128 \, a^{3}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{195 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^15/(b*x^4 + a)^(3/4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 23.6265, size = 92, normalized size = 1.18 \[ \begin{cases} - \frac{128 a^{3} \sqrt [4]{a + b x^{4}}}{195 b^{4}} + \frac{32 a^{2} x^{4} \sqrt [4]{a + b x^{4}}}{195 b^{3}} - \frac{4 a x^{8} \sqrt [4]{a + b x^{4}}}{39 b^{2}} + \frac{x^{12} \sqrt [4]{a + b x^{4}}}{13 b} & \text{for}\: b \neq 0 \\\frac{x^{16}}{16 a^{\frac{3}{4}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**15/(b*x**4+a)**(3/4),x)
[Out]
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GIAC/XCAS [A] time = 0.215635, size = 77, normalized size = 0.99 \[ \frac{15 \,{\left (b x^{4} + a\right )}^{\frac{13}{4}} - 65 \,{\left (b x^{4} + a\right )}^{\frac{9}{4}} a + 117 \,{\left (b x^{4} + a\right )}^{\frac{5}{4}} a^{2} - 195 \,{\left (b x^{4} + a\right )}^{\frac{1}{4}} a^{3}}{195 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^15/(b*x^4 + a)^(3/4),x, algorithm="giac")
[Out]