Optimal. Leaf size=13 \[ \frac {b x^n}{n}+a \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14}
\begin {gather*} a \log (x)+\frac {b x^n}{n} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^n}{x} \, dx &=\int \left (\frac {a}{x}+b x^{-1+n}\right ) \, dx\\ &=\frac {b x^n}{n}+a \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 18, normalized size = 1.38 \begin {gather*} \frac {b x^n}{n}+\frac {a \log \left (x^n\right )}{n} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 17, normalized size = 1.31
method | result | size |
risch | \(\frac {b \,x^{n}}{n}+a \ln \left (x \right )\) | \(14\) |
norman | \(a \ln \left (x \right )+\frac {b \,{\mathrm e}^{n \ln \left (x \right )}}{n}\) | \(16\) |
derivativedivides | \(\frac {b \,x^{n}+a \ln \left (x^{n}\right )}{n}\) | \(17\) |
default | \(\frac {b \,x^{n}+a \ln \left (x^{n}\right )}{n}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 18, normalized size = 1.38 \begin {gather*} \frac {b x^{n}}{n} + \frac {a \log \left (x^{n}\right )}{n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.48, size = 15, normalized size = 1.15 \begin {gather*} \frac {a n \log \left (x\right ) + b x^{n}}{n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 17, normalized size = 1.31 \begin {gather*} \begin {cases} a \log {\left (x \right )} + \frac {b x^{n}}{n} & \text {for}\: n \neq 0 \\\left (a + b\right ) \log {\left (x \right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.19, size = 13, normalized size = 1.00 \begin {gather*} a\,\ln \left (x\right )+\frac {b\,x^n}{n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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