Optimal. Leaf size=27 \[ \frac{a x^{2 n}}{2 n}+\frac{b x^{3 n}}{3 n} \]
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Rubi [A] time = 0.0223623, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{a x^{2 n}}{2 n}+\frac{b x^{3 n}}{3 n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 + 2*n)*(a + b*x^n),x]
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Rubi in Sympy [A] time = 4.01799, size = 19, normalized size = 0.7 \[ \frac{a x^{2 n}}{2 n} + \frac{b x^{3 n}}{3 n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+2*n)*(a+b*x**n),x)
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Mathematica [A] time = 0.00965357, size = 22, normalized size = 0.81 \[ \frac{x^{2 n} \left (3 a+2 b x^n\right )}{6 n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 + 2*n)*(a + b*x^n),x]
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Maple [A] time = 0.022, size = 28, normalized size = 1. \[{\frac{a \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{2}}{2\,n}}+{\frac{b \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{3}}{3\,n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+2*n)*(a+b*x^n),x)
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)*x^(2*n - 1),x, algorithm="maxima")
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Fricas [A] time = 0.223527, size = 30, normalized size = 1.11 \[ \frac{2 \, b x^{3 \, n} + 3 \, a x^{2 \, n}}{6 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)*x^(2*n - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 14.2686, size = 26, normalized size = 0.96 \[ \begin{cases} \frac{a x^{2 n}}{2 n} + \frac{b x^{3 n}}{3 n} & \text{for}\: n \neq 0 \\\left (a + b\right ) \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-1+2*n)*(a+b*x**n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x^{n} + a\right )} x^{2 \, n - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n + a)*x^(2*n - 1),x, algorithm="giac")
[Out]