Optimal. Leaf size=19 \[ \frac {(a+b \log (x))^{1+n}}{b (1+n)} \]
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Rubi [A]
time = 0.02, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2339, 30}
\begin {gather*} \frac {(a+b \log (x))^{n+1}}{b (n+1)} \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rule 2339
Rubi steps
\begin {align*} \int \frac {(a+b \log (x))^n}{x} \, dx &=\frac {\text {Subst}\left (\int x^n \, dx,x,a+b \log (x)\right )}{b}\\ &=\frac {(a+b \log (x))^{1+n}}{b (1+n)}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} \frac {(a+b \log (x))^{1+n}}{b (1+n)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 20, normalized size = 1.05
method | result | size |
derivativedivides | \(\frac {\left (a +b \ln \left (x \right )\right )^{1+n}}{b \left (1+n \right )}\) | \(20\) |
default | \(\frac {\left (a +b \ln \left (x \right )\right )^{1+n}}{b \left (1+n \right )}\) | \(20\) |
risch | \(\frac {\left (a +b \ln \left (x \right )\right ) \left (a +b \ln \left (x \right )\right )^{n}}{b \left (1+n \right )}\) | \(24\) |
norman | \(\frac {\ln \left (x \right ) {\mathrm e}^{n \ln \left (a +b \ln \left (x \right )\right )}}{1+n}+\frac {a \,{\mathrm e}^{n \ln \left (a +b \ln \left (x \right )\right )}}{b \left (1+n \right )}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 19, normalized size = 1.00 \begin {gather*} \frac {{\left (b \log \left (x\right ) + a\right )}^{n + 1}}{b {\left (n + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.61, size = 22, normalized size = 1.16 \begin {gather*} \frac {{\left (b \log \left (x\right ) + a\right )} {\left (b \log \left (x\right ) + a\right )}^{n}}{b n + b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.58, size = 36, normalized size = 1.89 \begin {gather*} - \begin {cases} - a^{n} \log {\left (x \right )} & \text {for}\: b = 0 \\- \frac {\begin {cases} \frac {\left (a + b \log {\left (x \right )}\right )^{n + 1}}{n + 1} & \text {for}\: n \neq -1 \\\log {\left (a + b \log {\left (x \right )} \right )} & \text {otherwise} \end {cases}}{b} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.78, size = 19, normalized size = 1.00 \begin {gather*} \frac {{\left (b \log \left (x\right ) + a\right )}^{n + 1}}{b {\left (n + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.45, size = 19, normalized size = 1.00 \begin {gather*} \frac {{\left (a+b\,\ln \left (x\right )\right )}^{n+1}}{b\,\left (n+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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