Optimal. Leaf size=22 \[ \frac{(b x)^{p+1} (c x)^m}{b (m+p+1)} \]
[Out]
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Rubi [A] time = 0.0227751, antiderivative size = 22, 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 \[ \frac{(b x)^{p+1} (c x)^m}{b (m+p+1)} \]
Antiderivative was successfully verified.
[In] Int[(b*x)^p*(c*x)^m,x]
[Out]
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Rubi in Sympy [A] time = 3.4361, size = 24, normalized size = 1.09 \[ \frac{\left (b x\right )^{- m} \left (b x\right )^{m + p + 1} \left (c x\right )^{m}}{b \left (m + p + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x)**p*(c*x)**m,x)
[Out]
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Mathematica [A] time = 0.00695899, size = 18, normalized size = 0.82 \[ \frac{x (b x)^p (c x)^m}{m+p+1} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x)^p*(c*x)^m,x]
[Out]
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Maple [A] time = 0.002, size = 19, normalized size = 0.9 \[{\frac{x \left ( bx \right ) ^{p} \left ( cx \right ) ^{m}}{1+m+p}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x)^p*(c*x)^m,x)
[Out]
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Maxima [A] time = 1.44001, size = 32, normalized size = 1.45 \[ \frac{b^{p} c^{m} x e^{\left (m \log \left (x\right ) + p \log \left (x\right )\right )}}{m + p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x)^p*(c*x)^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2681, size = 39, normalized size = 1.77 \[ \frac{\left (b x\right )^{p} x e^{\left (m \log \left (b x\right ) + m \log \left (\frac{c}{b}\right )\right )}}{m + p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x)^p*(c*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((b*x)**p*(c*x)**m,x)
[Out]
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GIAC/XCAS [A] time = 0.210412, size = 35, normalized size = 1.59 \[ \frac{x e^{\left (p{\rm ln}\left (b\right ) + m{\rm ln}\left (c\right ) + m{\rm ln}\left (x\right ) + p{\rm ln}\left (x\right )\right )}}{m + p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x)^p*(c*x)^m,x, algorithm="giac")
[Out]