Optimal. Leaf size=50 \[ a^3 \log (x)+\frac{3 a^2 b x^n}{n}+\frac{3 a b^2 x^{2 n}}{2 n}+\frac{b^3 x^{3 n}}{3 n} \]
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Rubi [A] time = 0.054967, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ a^3 \log (x)+\frac{3 a^2 b x^n}{n}+\frac{3 a b^2 x^{2 n}}{2 n}+\frac{b^3 x^{3 n}}{3 n} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^n)^3/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{3} \log{\left (x^{n} \right )}}{n} + \frac{3 a^{2} b x^{n}}{n} + \frac{3 a b^{2} \int ^{x^{n}} x\, dx}{n} + \frac{b^{3} x^{3 n}}{3 n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**n)**3/x,x)
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Mathematica [A] time = 0.0401134, size = 41, normalized size = 0.82 \[ a^3 \log (x)+\frac{b x^n \left (18 a^2+9 a b x^n+2 b^2 x^{2 n}\right )}{6 n} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^n)^3/x,x]
[Out]
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Maple [A] time = 0., size = 52, normalized size = 1. \[{\frac{{b}^{3} \left ({x}^{n} \right ) ^{3}}{3\,n}}+{\frac{3\,a{b}^{2} \left ({x}^{n} \right ) ^{2}}{2\,n}}+3\,{\frac{{a}^{2}b{x}^{n}}{n}}+{\frac{{a}^{3}\ln \left ({x}^{n} \right ) }{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^n)^3/x,x)
[Out]
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Maxima [A] time = 1.44071, size = 65, normalized size = 1.3 \[ \frac{a^{3} \log \left (x^{n}\right )}{n} + \frac{2 \, b^{3} x^{3 \, n} + 9 \, a b^{2} x^{2 \, n} + 18 \, a^{2} b x^{n}}{6 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^3/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226023, size = 59, normalized size = 1.18 \[ \frac{6 \, a^{3} n \log \left (x\right ) + 2 \, b^{3} x^{3 \, n} + 9 \, a b^{2} x^{2 \, n} + 18 \, a^{2} b x^{n}}{6 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^3/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.14972, size = 53, normalized size = 1.06 \[ \begin{cases} a^{3} \log{\left (x \right )} + \frac{3 a^{2} b x^{n}}{n} + \frac{3 a b^{2} x^{2 n}}{2 n} + \frac{b^{3} x^{3 n}}{3 n} & \text{for}\: n \neq 0 \\\left (a + b\right )^{3} \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**n)**3/x,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{n} + a\right )}^{3}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)^3/x,x, algorithm="giac")
[Out]