Optimal. Leaf size=21 \[ \frac{2}{5} a x^{5/2}+\frac{2}{7} b x^{7/2} \]
[Out]
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Rubi [A] time = 0.0131158, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{2}{5} a x^{5/2}+\frac{2}{7} b x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 2.32616, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00503557, size = 17, normalized size = 0.81 \[ \frac{2}{35} x^{5/2} (7 a+5 b x) \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(a + b*x),x]
[Out]
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \[{\frac{10\,bx+14\,a}{35}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(b*x+a),x)
[Out]
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Maxima [A] time = 1.34405, size = 18, normalized size = 0.86 \[ \frac{2}{7} \, b x^{\frac{7}{2}} + \frac{2}{5} \, a x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207841, size = 24, normalized size = 1.14 \[ \frac{2}{35} \,{\left (5 \, b x^{3} + 7 \, a x^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.02849, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.200362, size = 18, normalized size = 0.86 \[ \frac{2}{7} \, b x^{\frac{7}{2}} + \frac{2}{5} \, a x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^(3/2),x, algorithm="giac")
[Out]