Optimal. Leaf size=21 \[ \frac{x \left (a \left (b x^n\right )^p\right )^q}{n p q+1} \]
[Out]
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Rubi [A] time = 0.0304483, 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 \[ \frac{x \left (a \left (b x^n\right )^p\right )^q}{n p q+1} \]
Antiderivative was successfully verified.
[In] Int[(a*(b*x^n)^p)^q,x]
[Out]
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Rubi in Sympy [A] time = 2.51704, size = 31, normalized size = 1.48 \[ \frac{x^{- n p q} x^{n p q + 1} \left (a \left (b x^{n}\right )^{p}\right )^{q}}{n p q + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*(b*x**n)**p)**q,x)
[Out]
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Mathematica [A] time = 0.00541827, size = 21, normalized size = 1. \[ \frac{x \left (a \left (b x^n\right )^p\right )^q}{n p q+1} \]
Antiderivative was successfully verified.
[In] Integrate[(a*(b*x^n)^p)^q,x]
[Out]
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Maple [A] time = 0.002, size = 22, normalized size = 1.1 \[{\frac{x \left ( a \left ( b{x}^{n} \right ) ^{p} \right ) ^{q}}{npq+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*(b*x^n)^p)^q,x)
[Out]
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Maxima [A] time = 1.65177, size = 34, normalized size = 1.62 \[ \frac{a^{q}{\left (b^{p}\right )}^{q} x{\left ({\left (x^{n}\right )}^{p}\right )}^{q}}{n p q + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236525, size = 36, normalized size = 1.71 \[ \frac{x e^{\left (n p q \log \left (x\right ) + p q \log \left (b\right ) + q \log \left (a\right )\right )}}{n p q + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (a \left (b x^{n}\right )^{p}\right )^{q}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*(b*x**n)**p)**q,x)
[Out]
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GIAC/XCAS [A] time = 0.238163, size = 36, normalized size = 1.71 \[ \frac{x e^{\left (n p q{\rm ln}\left (x\right ) + p q{\rm ln}\left (b\right ) + q{\rm ln}\left (a\right )\right )}}{n p q + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((b*x^n)^p*a)^q,x, algorithm="giac")
[Out]