Optimal. Leaf size=19 \[ \frac{x^2 \left (b x^2\right )^p}{2 (p+1)} \]
[Out]
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Rubi [A] time = 0.0143378, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{x^2 \left (b x^2\right )^p}{2 (p+1)} \]
Antiderivative was successfully verified.
[In] Int[x*(b*x^2)^p,x]
[Out]
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Rubi in Sympy [A] time = 2.98443, size = 14, normalized size = 0.74 \[ \frac{\left (b x^{2}\right )^{p + 1}}{2 b \left (p + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(b*x**2)**p,x)
[Out]
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Mathematica [A] time = 0.00399403, size = 18, normalized size = 0.95 \[ \frac{x^2 \left (b x^2\right )^p}{2 p+2} \]
Antiderivative was successfully verified.
[In] Integrate[x*(b*x^2)^p,x]
[Out]
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Maple [A] time = 0.002, size = 18, normalized size = 1. \[{\frac{{x}^{2} \left ( b{x}^{2} \right ) ^{p}}{2+2\,p}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(b*x^2)^p,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235345, size = 23, normalized size = 1.21 \[ \frac{\left (b x^{2}\right )^{p} x^{2}}{2 \,{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.582597, size = 22, normalized size = 1.16 \[ \begin{cases} \frac{b^{p} x^{2} \left (x^{2}\right )^{p}}{2 p + 2} & \text{for}\: p \neq -1 \\\frac{\log{\left (x \right )}}{b} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(b*x**2)**p,x)
[Out]
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GIAC/XCAS [A] time = 0.222965, size = 26, normalized size = 1.37 \[ \frac{\left (b x^{2}\right )^{p + 1}}{2 \, b{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p*x,x, algorithm="giac")
[Out]