Optimal. Leaf size=21 \[ \frac{x^{m+1} \left (b x^n\right )^p}{m+n p+1} \]
[Out]
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Rubi [A] time = 0.0157806, 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 \[ \frac{x^{m+1} \left (b x^n\right )^p}{m+n p+1} \]
Antiderivative was successfully verified.
[In] Int[x^m*(b*x^n)^p,x]
[Out]
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Rubi in Sympy [A] time = 3.3874, size = 26, normalized size = 1.24 \[ \frac{x^{- n p} x^{m + n p + 1} \left (b x^{n}\right )^{p}}{m + n p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(b*x**n)**p,x)
[Out]
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Mathematica [A] time = 0.0079071, size = 21, normalized size = 1. \[ \frac{x^{m+1} \left (b x^n\right )^p}{m+n p+1} \]
Antiderivative was successfully verified.
[In] Integrate[x^m*(b*x^n)^p,x]
[Out]
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Maple [A] time = 0.003, size = 22, normalized size = 1.1 \[{\frac{{x}^{1+m} \left ( b{x}^{n} \right ) ^{p}}{np+m+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(b*x^n)^p,x)
[Out]
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Maxima [A] time = 1.45394, size = 34, normalized size = 1.62 \[ \frac{b^{p} x e^{\left (m \log \left (x\right ) + p \log \left (x^{n}\right )\right )}}{n p + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^p*x^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235055, size = 32, normalized size = 1.52 \[ \frac{x x^{m} e^{\left (n p \log \left (x\right ) + p \log \left (b\right )\right )}}{n p + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^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**n)**p,x)
[Out]
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GIAC/XCAS [A] time = 0.230086, size = 34, normalized size = 1.62 \[ \frac{x e^{\left (n p{\rm ln}\left (x\right ) + p{\rm ln}\left (b\right ) + m{\rm ln}\left (x\right )\right )}}{n p + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^p*x^m,x, algorithm="giac")
[Out]