Optimal. Leaf size=34 \[ \frac{x \left (c x^n\right )^{-1/n} \left (a+b \left (c x^n\right )^{\frac{1}{n}}\right )^3}{3 b} \]
[Out]
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Rubi [A] time = 0.0217195, antiderivative size = 34, 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 \[ \frac{x \left (c x^n\right )^{-1/n} \left (a+b \left (c x^n\right )^{\frac{1}{n}}\right )^3}{3 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b*(c*x^n)^n^(-1))^2,x]
[Out]
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Rubi in Sympy [A] time = 2.30416, size = 26, normalized size = 0.76 \[ \frac{x \left (c x^{n}\right )^{- \frac{1}{n}} \left (a + b \left (c x^{n}\right )^{\frac{1}{n}}\right )^{3}}{3 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*(c*x**n)**(1/n))**2,x)
[Out]
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Mathematica [A] time = 0.0239098, size = 34, normalized size = 1. \[ \frac{x \left (c x^n\right )^{-1/n} \left (a+b \left (c x^n\right )^{\frac{1}{n}}\right )^3}{3 b} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*(c*x^n)^n^(-1))^2,x]
[Out]
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Maple [F] time = 0.043, size = 0, normalized size = 0. \[ \int \left ( a+b\sqrt [n]{c{x}^{n}} \right ) ^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*(c*x^n)^(1/n))^2,x)
[Out]
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Maxima [A] time = 1.42503, size = 43, normalized size = 1.26 \[ \frac{1}{3} \, b^{2} c^{\frac{2}{n}} x^{3} + a b c^{\left (\frac{1}{n}\right )} x^{2} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((c*x^n)^(1/n)*b + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233443, size = 43, normalized size = 1.26 \[ \frac{1}{3} \, b^{2} c^{\frac{2}{n}} x^{3} + a b c^{\left (\frac{1}{n}\right )} x^{2} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((c*x^n)^(1/n)*b + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.19122, size = 39, normalized size = 1.15 \[ a^{2} x + a b c^{\frac{1}{n}} x \left (x^{n}\right )^{\frac{1}{n}} + \frac{b^{2} c^{\frac{2}{n}} x \left (x^{n}\right )^{\frac{2}{n}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*(c*x**n)**(1/n))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.227086, size = 47, normalized size = 1.38 \[ \frac{1}{3} \, b^{2} x^{3} e^{\left (\frac{2 \,{\rm ln}\left (c\right )}{n}\right )} + a b x^{2} e^{\left (\frac{{\rm ln}\left (c\right )}{n}\right )} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((c*x^n)^(1/n)*b + a)^2,x, algorithm="giac")
[Out]