Optimal. Leaf size=26 \[ \frac{x^{m+1} \left (a \left (b x^n\right )^p\right )^q}{m+n p q+1} \]
[Out]
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Rubi [A] time = 0.080876, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{x^{m+1} \left (a \left (b x^n\right )^p\right )^q}{m+n p q+1} \]
Antiderivative was successfully verified.
[In] Int[x^m*(a*(b*x^n)^p)^q,x]
[Out]
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Rubi in Sympy [A] time = 7.05711, size = 34, normalized size = 1.31 \[ \frac{x^{- n p q} x^{m + n p q + 1} \left (a \left (b x^{n}\right )^{p}\right )^{q}}{m + n p q + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(a*(b*x**n)**p)**q,x)
[Out]
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Mathematica [A] time = 0.0172672, size = 26, normalized size = 1. \[ \frac{x^{m+1} \left (a \left (b x^n\right )^p\right )^q}{m+n p q+1} \]
Antiderivative was successfully verified.
[In] Integrate[x^m*(a*(b*x^n)^p)^q,x]
[Out]
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Maple [A] time = 0.003, size = 27, normalized size = 1. \[{\frac{{x}^{1+m} \left ( a \left ( b{x}^{n} \right ) ^{p} \right ) ^{q}}{npq+m+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(a*(b*x^n)^p)^q,x)
[Out]
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Maxima [A] time = 1.64882, size = 45, normalized size = 1.73 \[ \frac{a^{q}{\left (b^{p}\right )}^{q} x e^{\left (m \log \left (x\right ) + q \log \left ({\left (x^{n}\right )}^{p}\right )\right )}}{n p q + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q*x^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235759, size = 42, normalized size = 1.62 \[ \frac{x x^{m} e^{\left (n p q \log \left (x\right ) + p q \log \left (b\right ) + q \log \left (a\right )\right )}}{n p q + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q*x^m,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m*(a*(b*x**n)**p)**q,x)
[Out]
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GIAC/XCAS [A] time = 0.224601, size = 43, normalized size = 1.65 \[ \frac{x e^{\left (n p q{\rm ln}\left (x\right ) + p q{\rm ln}\left (b\right ) + q{\rm ln}\left (a\right ) + m{\rm ln}\left (x\right )\right )}}{n p q + m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q*x^m,x, algorithm="giac")
[Out]