Optimal. Leaf size=27 \[ \frac {F^{a+b (c+d x)^3}}{3 b d \log (F)} \]
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Rubi [A]
time = 0.05, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2240}
\begin {gather*} \frac {F^{a+b (c+d x)^3}}{3 b d \log (F)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2240
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^3} (c+d x)^2 \, dx &=\frac {F^{a+b (c+d x)^3}}{3 b d \log (F)}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 27, normalized size = 1.00 \begin {gather*} \frac {F^{a+b (c+d x)^3}}{3 b d \log (F)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 26, normalized size = 0.96
method | result | size |
derivativedivides | \(\frac {F^{a +b \left (d x +c \right )^{3}}}{3 b d \ln \left (F \right )}\) | \(26\) |
default | \(\frac {F^{a +b \left (d x +c \right )^{3}}}{3 b d \ln \left (F \right )}\) | \(26\) |
norman | \(\frac {{\mathrm e}^{\left (a +b \left (d x +c \right )^{3}\right ) \ln \left (F \right )}}{3 b \ln \left (F \right ) d}\) | \(28\) |
gosper | \(\frac {F^{b \,d^{3} x^{3}+3 b c \,d^{2} x^{2}+3 b \,c^{2} d x +b \,c^{3}+a}}{3 b d \ln \left (F \right )}\) | \(48\) |
risch | \(\frac {F^{b \,d^{3} x^{3}+3 b c \,d^{2} x^{2}+3 b \,c^{2} d x +b \,c^{3}+a}}{3 b d \ln \left (F \right )}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 25, normalized size = 0.93 \begin {gather*} \frac {F^{{\left (d x + c\right )}^{3} b + a}}{3 \, b d \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 47, normalized size = 1.74 \begin {gather*} \frac {F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}}{3 \, b d \log \left (F\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. 44 vs.
\(2 (19) = 38\).
time = 0.06, size = 44, normalized size = 1.63 \begin {gather*} \begin {cases} \frac {F^{a + b \left (c + d x\right )^{3}}}{3 b d \log {\left (F \right )}} & \text {for}\: b d \log {\left (F \right )} \neq 0 \\c^{2} x + c d x^{2} + \frac {d^{2} x^{3}}{3} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.97, size = 47, normalized size = 1.74 \begin {gather*} \frac {F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}}{3 \, b d \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.53, size = 25, normalized size = 0.93 \begin {gather*} \frac {F^{a+b\,{\left (c+d\,x\right )}^3}}{3\,b\,d\,\ln \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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