Optimal. Leaf size=38 \[ \frac{a}{2 b^2 \sqrt{a+b x^4}}+\frac{\sqrt{a+b x^4}}{2 b^2} \]
[Out]
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Rubi [A] time = 0.0582628, 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 \[ \frac{a}{2 b^2 \sqrt{a+b x^4}}+\frac{\sqrt{a+b x^4}}{2 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^7/(a + b*x^4)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 7.10198, size = 31, normalized size = 0.82 \[ \frac{a}{2 b^{2} \sqrt{a + b x^{4}}} + \frac{\sqrt{a + b x^{4}}}{2 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(b*x**4+a)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0253046, size = 27, normalized size = 0.71 \[ \frac{2 a+b x^4}{2 b^2 \sqrt{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^7/(a + b*x^4)^(3/2),x]
[Out]
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Maple [A] time = 0.007, size = 24, normalized size = 0.6 \[{\frac{b{x}^{4}+2\,a}{2\,{b}^{2}}{\frac{1}{\sqrt{b{x}^{4}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(b*x^4+a)^(3/2),x)
[Out]
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Maxima [A] time = 1.44289, size = 41, normalized size = 1.08 \[ \frac{\sqrt{b x^{4} + a}}{2 \, b^{2}} + \frac{a}{2 \, \sqrt{b x^{4} + a} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(b*x^4 + a)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253775, size = 31, normalized size = 0.82 \[ \frac{b x^{4} + 2 \, a}{2 \, \sqrt{b x^{4} + a} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(b*x^4 + a)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.00967, size = 41, normalized size = 1.08 \[ \begin{cases} \frac{a}{b^{2} \sqrt{a + b x^{4}}} + \frac{x^{4}}{2 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{8}}{8 a^{\frac{3}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(b*x**4+a)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216919, size = 35, normalized size = 0.92 \[ \frac{\sqrt{b x^{4} + a} + \frac{a}{\sqrt{b x^{4} + a}}}{2 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(b*x^4 + a)^(3/2),x, algorithm="giac")
[Out]