Optimal. Leaf size=38 \[ \frac{\left (a+b x^4\right )^{7/4}}{7 b^2}-\frac{a \left (a+b x^4\right )^{3/4}}{3 b^2} \]
[Out]
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Rubi [A] time = 0.0592666, antiderivative size = 38, 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 \[ \frac{\left (a+b x^4\right )^{7/4}}{7 b^2}-\frac{a \left (a+b x^4\right )^{3/4}}{3 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^7/(a + b*x^4)^(1/4),x]
[Out]
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Rubi in Sympy [A] time = 7.03994, size = 31, normalized size = 0.82 \[ - \frac{a \left (a + b x^{4}\right )^{\frac{3}{4}}}{3 b^{2}} + \frac{\left (a + b x^{4}\right )^{\frac{7}{4}}}{7 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(b*x**4+a)**(1/4),x)
[Out]
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Mathematica [A] time = 0.0243971, size = 28, normalized size = 0.74 \[ \frac{\left (a+b x^4\right )^{3/4} \left (3 b x^4-4 a\right )}{21 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^7/(a + b*x^4)^(1/4),x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 0.7 \[ -{\frac{-3\,b{x}^{4}+4\,a}{21\,{b}^{2}} \left ( b{x}^{4}+a \right ) ^{{\frac{3}{4}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(b*x^4+a)^(1/4),x)
[Out]
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Maxima [A] time = 1.44955, size = 41, normalized size = 1.08 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{7}{4}}}{7 \, b^{2}} - \frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}} a}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(b*x^4 + a)^(1/4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269957, size = 32, normalized size = 0.84 \[ \frac{{\left (3 \, b x^{4} - 4 \, a\right )}{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{21 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(b*x^4 + a)^(1/4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.23873, size = 44, normalized size = 1.16 \[ \begin{cases} - \frac{4 a \left (a + b x^{4}\right )^{\frac{3}{4}}}{21 b^{2}} + \frac{x^{4} \left (a + b x^{4}\right )^{\frac{3}{4}}}{7 b} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 \sqrt [4]{a}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(b*x**4+a)**(1/4),x)
[Out]
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GIAC/XCAS [A] time = 0.215455, size = 39, normalized size = 1.03 \[ \frac{3 \,{\left (b x^{4} + a\right )}^{\frac{7}{4}} - 7 \,{\left (b x^{4} + a\right )}^{\frac{3}{4}} a}{21 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(b*x^4 + a)^(1/4),x, algorithm="giac")
[Out]