Optimal. Leaf size=24 \[ \frac {\left (a+b F^x\right )^{n+1}}{b (n+1) \log (F)} \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2246, 32} \[ \frac {\left (a+b F^x\right )^{n+1}}{b (n+1) \log (F)} \]
Antiderivative was successfully verified.
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Rule 32
Rule 2246
Rubi steps
\begin {align*} \int F^x \left (a+b F^x\right )^n \, dx &=\frac {\operatorname {Subst}\left (\int (a+b x)^n \, dx,x,F^x\right )}{\log (F)}\\ &=\frac {\left (a+b F^x\right )^{1+n}}{b (1+n) \log (F)}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 24, normalized size = 1.00 \[ \frac {\left (a+b F^x\right )^{n+1}}{b n \log (F)+b \log (F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 28, normalized size = 1.17 \[ \frac {{\left (F^{x} b + a\right )} {\left (F^{x} b + a\right )}^{n}}{{\left (b n + b\right )} \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 24, normalized size = 1.00 \[ \frac {{\left (F^{x} b + a\right )}^{n + 1}}{b {\left (n + 1\right )} \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 1.04 \[ \frac {\left (b \,F^{x}+a \right )^{n +1}}{\left (n +1\right ) b \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 24, normalized size = 1.00 \[ \frac {{\left (F^{x} b + a\right )}^{n + 1}}{b {\left (n + 1\right )} \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.48, size = 24, normalized size = 1.00 \[ \frac {{\left (a+F^x\,b\right )}^{n+1}}{b\,\ln \relax (F)\,\left (n+1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.26, size = 82, normalized size = 3.42 \[ \begin {cases} \frac {x}{a} & \text {for}\: F = 1 \wedge b = 0 \wedge n = -1 \\x \left (a + b\right )^{n} & \text {for}\: F = 1 \\\frac {F^{x} a^{n}}{\log {\relax (F )}} & \text {for}\: b = 0 \\\frac {\log {\left (F^{x} + \frac {a}{b} \right )}}{b \log {\relax (F )}} & \text {for}\: n = -1 \\\frac {F^{x} b \left (F^{x} b + a\right )^{n}}{b n \log {\relax (F )} + b \log {\relax (F )}} + \frac {a \left (F^{x} b + a\right )^{n}}{b n \log {\relax (F )} + b \log {\relax (F )}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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