Optimal. Leaf size=21 \[ \frac {a x^4}{4}+\frac {b x^{4+n}}{4+n} \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14}
\begin {gather*} \frac {a x^4}{4}+\frac {b x^{n+4}}{n+4} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x^3 \left (a+b x^n\right ) \, dx &=\int \left (a x^3+b x^{3+n}\right ) \, dx\\ &=\frac {a x^4}{4}+\frac {b x^{4+n}}{4+n}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 21, normalized size = 1.00 \begin {gather*} \frac {a x^4}{4}+\frac {b x^{4+n}}{4+n} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 21, normalized size = 1.00
method | result | size |
risch | \(\frac {b \,x^{4} x^{n}}{4+n}+\frac {a \,x^{4}}{4}\) | \(21\) |
norman | \(\frac {b \,x^{4} {\mathrm e}^{n \ln \left (x \right )}}{4+n}+\frac {a \,x^{4}}{4}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 19, normalized size = 0.90 \begin {gather*} \frac {1}{4} \, a x^{4} + \frac {b x^{n + 4}}{n + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.49, size = 28, normalized size = 1.33 \begin {gather*} \frac {4 \, b x^{4} x^{n} + {\left (a n + 4 \, a\right )} x^{4}}{4 \, {\left (n + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (15) = 30\).
time = 0.14, size = 51, normalized size = 2.43 \begin {gather*} \begin {cases} \frac {a n x^{4}}{4 n + 16} + \frac {4 a x^{4}}{4 n + 16} + \frac {4 b x^{4} x^{n}}{4 n + 16} & \text {for}\: n \neq -4 \\\frac {a x^{4}}{4} + b \log {\left (x \right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.04, size = 29, normalized size = 1.38 \begin {gather*} \frac {4 \, b x^{4} x^{n} + a n x^{4} + 4 \, a x^{4}}{4 \, {\left (n + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.33, size = 20, normalized size = 0.95 \begin {gather*} \frac {a\,x^4}{4}+\frac {b\,x^n\,x^4}{n+4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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