Integrand size = 9, antiderivative size = 8 \[ \int \frac {a+b x}{x} \, dx=b x+a \log (x) \]
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Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45} \[ \int \frac {a+b x}{x} \, dx=a \log (x)+b x \]
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Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (b+\frac {a}{x}\right ) \, dx \\ & = b x+a \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {a+b x}{x} \, dx=b x+a \log (x) \]
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Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.12
method | result | size |
default | \(b x +a \ln \left (x \right )\) | \(9\) |
norman | \(b x +a \ln \left (x \right )\) | \(9\) |
risch | \(b x +a \ln \left (x \right )\) | \(9\) |
parallelrisch | \(b x +a \ln \left (x \right )\) | \(9\) |
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none
Time = 0.22 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {a+b x}{x} \, dx=b x + a \log \left (x\right ) \]
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Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {a+b x}{x} \, dx=a \log {\left (x \right )} + b x \]
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none
Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {a+b x}{x} \, dx=b x + a \log \left (x\right ) \]
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none
Time = 0.30 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.12 \[ \int \frac {a+b x}{x} \, dx=b x + a \log \left ({\left | x \right |}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {a+b x}{x} \, dx=b\,x+a\,\ln \left (x\right ) \]
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