Optimal. Leaf size=15 \[ \frac {F^{a+b x}}{b \log (F)} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2225}
\begin {gather*} \frac {F^{a+b x}}{b \log (F)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rubi steps
\begin {align*} \int F^{a+b x} \, dx &=\frac {F^{a+b x}}{b \log (F)}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} \frac {F^{a+b x}}{b \log (F)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 16, normalized size = 1.07
method | result | size |
gosper | \(\frac {F^{b x +a}}{b \ln \left (F \right )}\) | \(16\) |
derivativedivides | \(\frac {F^{b x +a}}{b \ln \left (F \right )}\) | \(16\) |
default | \(\frac {F^{b x +a}}{b \ln \left (F \right )}\) | \(16\) |
risch | \(\frac {F^{b x +a}}{b \ln \left (F \right )}\) | \(16\) |
norman | \(\frac {{\mathrm e}^{\left (b x +a \right ) \ln \left (F \right )}}{b \ln \left (F \right )}\) | \(18\) |
meijerg | \(-\frac {F^{a} \left (1-{\mathrm e}^{x b \ln \left (F \right )}\right )}{b \ln \left (F \right )}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 15, normalized size = 1.00 \begin {gather*} \frac {F^{b x + a}}{b \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.47, size = 15, normalized size = 1.00 \begin {gather*} \frac {F^{b x + a}}{b \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 1.00 \begin {gather*} \begin {cases} \frac {F^{a + b x}}{b \log {\left (F \right )}} & \text {for}\: b \log {\left (F \right )} \neq 0 \\x & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.29, size = 15, normalized size = 1.00 \begin {gather*} \frac {F^{b x + a}}{b \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.44, size = 15, normalized size = 1.00 \begin {gather*} \frac {F^{a+b\,x}}{b\,\ln \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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