Optimal. Leaf size=26 \[ \frac{(c x)^{m+1} \left (b x^n\right )^p}{c (m+n p+1)} \]
[Out]
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Rubi [A] time = 0.016426, antiderivative size = 22, normalized size of antiderivative = 0.85, number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{x (c x)^m \left (b x^n\right )^p}{m+n p+1} \]
Antiderivative was successfully verified.
[In] Int[(c*x)^m*(b*x^n)^p,x]
[Out]
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Rubi in Sympy [A] time = 4.97659, size = 34, normalized size = 1.31 \[ \frac{x^{- m} x^{- n p} x^{m + n p + 1} \left (b x^{n}\right )^{p} \left (c x\right )^{m}}{m + n p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x)**m*(b*x**n)**p,x)
[Out]
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Mathematica [A] time = 0.0072297, size = 22, normalized size = 0.85 \[ \frac{x (c x)^m \left (b x^n\right )^p}{m+n p+1} \]
Antiderivative was successfully verified.
[In] Integrate[(c*x)^m*(b*x^n)^p,x]
[Out]
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Maple [A] time = 0.001, size = 23, normalized size = 0.9 \[{\frac{x \left ( cx \right ) ^{m} \left ( b{x}^{n} \right ) ^{p}}{np+m+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x)^m*(b*x^n)^p,x)
[Out]
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Maxima [A] time = 1.44685, size = 38, normalized size = 1.46 \[ \frac{b^{p} c^{m} x e^{\left (m \log \left (x\right ) + p \log \left (x^{n}\right )\right )}}{n p + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^m*(b*x^n)^p,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.252716, size = 39, normalized size = 1.5 \[ \frac{x e^{\left (n p \log \left (x\right ) + p \log \left (b\right ) + m \log \left (c\right ) + m \log \left (x\right )\right )}}{n p + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^m*(b*x^n)^p,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((c*x)**m*(b*x**n)**p,x)
[Out]
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GIAC/XCAS [A] time = 0.231311, size = 39, normalized size = 1.5 \[ \frac{x e^{\left (n p{\rm ln}\left (x\right ) + p{\rm ln}\left (b\right ) + m{\rm ln}\left (c\right ) + m{\rm ln}\left (x\right )\right )}}{n p + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^m*(b*x^n)^p,x, algorithm="giac")
[Out]