Optimal. Leaf size=27 \[ \frac {a x^{3 n}}{3 n}+\frac {b x^{4 n}}{4 n} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14} \[ \frac {a x^{3 n}}{3 n}+\frac {b x^{4 n}}{4 n} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x^{-1+3 n} \left (a+b x^n\right ) \, dx &=\int \left (a x^{-1+3 n}+b x^{-1+4 n}\right ) \, dx\\ &=\frac {a x^{3 n}}{3 n}+\frac {b x^{4 n}}{4 n}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 0.81 \[ \frac {x^{3 n} \left (4 a+3 b x^n\right )}{12 n} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 22, normalized size = 0.81 \[ \frac {3 \, b x^{4 \, n} + 4 \, a x^{3 \, n}}{12 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b x^{n} + a\right )} x^{3 \, n - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 28, normalized size = 1.04 \[ \frac {a \,{\mathrm e}^{3 n \ln \relax (x )}}{3 n}+\frac {b \,{\mathrm e}^{4 n \ln \relax (x )}}{4 n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 23, normalized size = 0.85 \[ \frac {b x^{4 \, n}}{4 \, n} + \frac {a x^{3 \, n}}{3 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.27, size = 20, normalized size = 0.74 \[ \frac {x^{3\,n}\,\left (4\,a+3\,b\,x^n\right )}{12\,n} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.70, size = 26, normalized size = 0.96 \[ \begin {cases} \frac {a x^{3 n}}{3 n} + \frac {b x^{4 n}}{4 n} & \text {for}\: n \neq 0 \\\left (a + b\right ) \log {\relax (x )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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