Optimal. Leaf size=27 \[ \frac {F^{a+b (c+d x)^n}}{b d n \log (F)} \]
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Rubi [A]
time = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2240}
\begin {gather*} \frac {F^{a+b (c+d x)^n}}{b d n \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)^n} (c+d x)^{-1+n} \, dx &=\frac {F^{a+b (c+d x)^n}}{b d n \log (F)}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 1.00 \begin {gather*} \frac {F^{a+b (c+d x)^n}}{b d n \log (F)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 28, normalized size = 1.04
method | result | size |
risch | \(\frac {F^{a +b \left (d x +c \right )^{n}}}{b d n \ln \left (F \right )}\) | \(28\) |
norman | \(\frac {{\mathrm e}^{\left (a +b \,{\mathrm e}^{n \ln \left (d x +c \right )}\right ) \ln \left (F \right )}}{d b n \ln \left (F \right )}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 27, normalized size = 1.00 \begin {gather*} \frac {F^{{\left (d x + c\right )}^{n} b + a}}{b d n \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 31, normalized size = 1.15 \begin {gather*} \frac {e^{\left ({\left (d x + c\right )}^{n} b \log \left (F\right ) + a \log \left (F\right )\right )}}{b d n \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.08, size = 27, normalized size = 1.00 \begin {gather*} \frac {F^{{\left (d x + c\right )}^{n} b + a}}{b d n \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.68, size = 27, normalized size = 1.00 \begin {gather*} \frac {F^{a+b\,{\left (c+d\,x\right )}^n}}{b\,d\,n\,\ln \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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