Optimal. Leaf size=43 \[ a^2 x+\frac{1}{2} a b x \left (c x^n\right )^{3/n}+\frac{1}{7} b^2 x \left (c x^n\right )^{6/n} \]
[Out]
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Rubi [A] time = 0.0351556, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ a^2 x+\frac{1}{2} a b x \left (c x^n\right )^{3/n}+\frac{1}{7} b^2 x \left (c x^n\right )^{6/n} \]
Antiderivative was successfully verified.
[In] Int[(a + b*(c*x^n)^(3/n))^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a b x \left (c x^{n}\right )^{\frac{3}{n}}}{2} + \frac{b^{2} x \left (c x^{n}\right )^{\frac{6}{n}}}{7} + x \left (c x^{n}\right )^{- \frac{1}{n}} \int ^{\left (c x^{n}\right )^{\frac{1}{n}}} a^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*(c*x**n)**(3/n))**2,x)
[Out]
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Mathematica [A] time = 0.124356, size = 43, normalized size = 1. \[ a^2 x+\frac{1}{2} a b x \left (c x^n\right )^{3/n}+\frac{1}{7} b^2 x \left (c x^n\right )^{6/n} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*(c*x^n)^(3/n))^2,x]
[Out]
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Maple [F] time = 0.039, size = 0, normalized size = 0. \[ \int \left ( a+b \left ( c{x}^{n} \right ) ^{3\,{n}^{-1}} \right ) ^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*(c*x^n)^(3/n))^2,x)
[Out]
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Maxima [A] time = 1.44237, size = 47, normalized size = 1.09 \[ \frac{1}{7} \, b^{2} c^{\frac{6}{n}} x^{7} + \frac{1}{2} \, a b c^{\frac{3}{n}} x^{4} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((c*x^n)^(3/n)*b + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247586, size = 47, normalized size = 1.09 \[ \frac{1}{7} \, b^{2} c^{\frac{6}{n}} x^{7} + \frac{1}{2} \, a b c^{\frac{3}{n}} x^{4} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((c*x^n)^(3/n)*b + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.24158, size = 41, normalized size = 0.95 \[ a^{2} x + \frac{a b c^{\frac{3}{n}} x \left (x^{n}\right )^{\frac{3}{n}}}{2} + \frac{b^{2} c^{\frac{6}{n}} x \left (x^{n}\right )^{\frac{6}{n}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*(c*x**n)**(3/n))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.222746, size = 50, normalized size = 1.16 \[ \frac{1}{7} \, b^{2} x^{7} e^{\left (\frac{6 \,{\rm ln}\left (c\right )}{n}\right )} + \frac{1}{2} \, a b x^{4} e^{\left (\frac{3 \,{\rm ln}\left (c\right )}{n}\right )} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((c*x^n)^(3/n)*b + a)^2,x, algorithm="giac")
[Out]