Optimal. Leaf size=20 \[ \frac {f^{a+b x^n}}{b n \log (f)} \]
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Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2209} \[ \frac {f^{a+b x^n}}{b n \log (f)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int f^{a+b x^n} x^{-1+n} \, dx &=\frac {f^{a+b x^n}}{b n \log (f)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \[ \frac {f^{a+b x^n}}{b n \log (f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 24, normalized size = 1.20 \[ \frac {e^{\left (b x^{n} \log \relax (f) + a \log \relax (f)\right )}}{b n \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 20, normalized size = 1.00 \[ \frac {f^{b x^{n} + a}}{b n \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 25, normalized size = 1.25 \[ \frac {{\mathrm e}^{\left (b \,{\mathrm e}^{n \ln \relax (x )}+a \right ) \ln \relax (f )}}{b n \ln \relax (f )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 20, normalized size = 1.00 \[ \frac {f^{b x^{n} + a}}{b n \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 20, normalized size = 1.00 \[ \frac {f^{a+b\,x^n}}{b\,n\,\ln \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 67.28, size = 39, normalized size = 1.95 \[ \begin {cases} \log {\relax (x )} & \text {for}\: b = 0 \wedge f = 1 \wedge n = 0 \\f^{a + b} \log {\relax (x )} & \text {for}\: n = 0 \\\frac {f^{a} x^{n}}{n} & \text {for}\: b = 0 \\\frac {x^{n}}{n} & \text {for}\: f = 1 \\\frac {f^{a} f^{b x^{n}}}{b n \log {\relax (f )}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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