Optimal. Leaf size=21 \[ \frac{x^{m+1} \left (b x^2\right )^p}{m+2 p+1} \]
[Out]
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Rubi [A] time = 0.0154517, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{x^{m+1} \left (b x^2\right )^p}{m+2 p+1} \]
Antiderivative was successfully verified.
[In] Int[x^m*(b*x^2)^p,x]
[Out]
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Rubi in Sympy [A] time = 3.10991, size = 26, normalized size = 1.24 \[ \frac{x^{- 2 p} x^{m + 2 p + 1} \left (b x^{2}\right )^{p}}{m + 2 p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(b*x**2)**p,x)
[Out]
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Mathematica [A] time = 0.00699259, size = 21, normalized size = 1. \[ \frac{x^{m+1} \left (b x^2\right )^p}{m+2 p+1} \]
Antiderivative was successfully verified.
[In] Integrate[x^m*(b*x^2)^p,x]
[Out]
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Maple [A] time = 0.004, size = 22, normalized size = 1.1 \[{\frac{{x}^{1+m} \left ( b{x}^{2} \right ) ^{p}}{1+m+2\,p}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(b*x^2)^p,x)
[Out]
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Maxima [A] time = 1.44795, size = 32, normalized size = 1.52 \[ \frac{b^{p} x e^{\left (m \log \left (x\right ) + 2 \, p \log \left (x\right )\right )}}{m + 2 \, p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p*x^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234499, size = 32, normalized size = 1.52 \[ \frac{x x^{m} e^{\left (p \log \left (b\right ) + 2 \, p \log \left (x\right )\right )}}{m + 2 \, p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p*x^m,x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m*(b*x**2)**p,x)
[Out]
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GIAC/XCAS [A] time = 0.213962, size = 34, normalized size = 1.62 \[ \frac{x e^{\left (p{\rm ln}\left (b\right ) + m{\rm ln}\left (x\right ) + 2 \, p{\rm ln}\left (x\right )\right )}}{m + 2 \, p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p*x^m,x, algorithm="giac")
[Out]