Optimal. Leaf size=38 \[ \frac{3 a}{2 b^2 \sqrt [3]{a+b x^2}}+\frac{3 \left (a+b x^2\right )^{2/3}}{4 b^2} \]
[Out]
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Rubi [A] time = 0.070699, 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 \[ \frac{3 a}{2 b^2 \sqrt [3]{a+b x^2}}+\frac{3 \left (a+b x^2\right )^{2/3}}{4 b^2} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a + b*x^2)^(4/3),x]
[Out]
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Rubi in Sympy [A] time = 7.83016, size = 34, normalized size = 0.89 \[ \frac{3 a}{2 b^{2} \sqrt [3]{a + b x^{2}}} + \frac{3 \left (a + b x^{2}\right )^{\frac{2}{3}}}{4 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(b*x**2+a)**(4/3),x)
[Out]
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Mathematica [A] time = 0.0238519, size = 27, normalized size = 0.71 \[ \frac{3 \left (3 a+b x^2\right )}{4 b^2 \sqrt [3]{a+b x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a + b*x^2)^(4/3),x]
[Out]
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Maple [A] time = 0.007, size = 24, normalized size = 0.6 \[{\frac{3\,b{x}^{2}+9\,a}{4\,{b}^{2}}{\frac{1}{\sqrt [3]{b{x}^{2}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(b*x^2+a)^(4/3),x)
[Out]
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Maxima [A] time = 1.47639, size = 41, normalized size = 1.08 \[ \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{2}{3}}}{4 \, b^{2}} + \frac{3 \, a}{2 \,{\left (b x^{2} + a\right )}^{\frac{1}{3}} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^2 + a)^(4/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214525, size = 31, normalized size = 0.82 \[ \frac{3 \,{\left (b x^{2} + 3 \, a\right )}}{4 \,{\left (b x^{2} + a\right )}^{\frac{1}{3}} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^2 + a)^(4/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.46287, size = 46, normalized size = 1.21 \[ \begin{cases} \frac{9 a}{4 b^{2} \sqrt [3]{a + b x^{2}}} + \frac{3 x^{2}}{4 b \sqrt [3]{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{4}{3}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(b*x**2+a)**(4/3),x)
[Out]
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GIAC/XCAS [A] time = 0.213392, size = 36, normalized size = 0.95 \[ \frac{3 \,{\left ({\left (b x^{2} + a\right )}^{\frac{2}{3}} + \frac{2 \, a}{{\left (b x^{2} + a\right )}^{\frac{1}{3}}}\right )}}{4 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*x^2 + a)^(4/3),x, algorithm="giac")
[Out]