Optimal. Leaf size=10 \[ \frac {\log (a+b x)}{b} \]
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Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {27, 31} \[ \frac {\log (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 27
Rule 31
Rubi steps
\begin {align*} \int \frac {a+b x}{a^2+2 a b x+b^2 x^2} \, dx &=\int \frac {1}{a+b x} \, dx\\ &=\frac {\log (a+b x)}{b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \[ \frac {\log (a+b x)}{b} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.03, size = 10, normalized size = 1.00 \[ \frac {\log \left (b x + a\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 22, normalized size = 2.20 \[ \frac {\log \left (a^{2} + {\left (b x^{2} + 2 \, a x\right )} b\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 11, normalized size = 1.10 \[ \frac {\ln \left (b x +a \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.53, size = 22, normalized size = 2.20 \[ \frac {\log \left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 10, normalized size = 1.00 \[ \frac {\ln \left (a+b\,x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 7, normalized size = 0.70 \[ \frac {\log {\left (a + b x \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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