Optimal. Leaf size=11 \[ -\frac {a}{x}+b \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45}
\begin {gather*} b \log (x)-\frac {a}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {a+b x}{x^2} \, dx &=\int \left (\frac {a}{x^2}+\frac {b}{x}\right ) \, dx\\ &=-\frac {a}{x}+b \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} -\frac {a}{x}+b \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 1.09
method | result | size |
default | \(-\frac {a}{x}+b \ln \left (x \right )\) | \(12\) |
norman | \(-\frac {a}{x}+b \ln \left (x \right )\) | \(12\) |
risch | \(-\frac {a}{x}+b \ln \left (x \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 11, normalized size = 1.00 \begin {gather*} b \log \left (x\right ) - \frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.67, size = 13, normalized size = 1.18 \begin {gather*} \frac {b x \log \left (x\right ) - a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.64 \begin {gather*} - \frac {a}{x} + b \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.48, size = 12, normalized size = 1.09 \begin {gather*} b \log \left ({\left | x \right |}\right ) - \frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 11, normalized size = 1.00 \begin {gather*} b\,\ln \left (x\right )-\frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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