Optimal. Leaf size=31 \[ -\frac {1}{b (a+b x)}-\frac {\log (a+b x)}{b (a+b x)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2390, 2304} \[ -\frac {1}{b (a+b x)}-\frac {\log (a+b x)}{b (a+b x)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2304
Rule 2390
Rubi steps
\begin {align*} \int \frac {\log (a+b x)}{(a+b x)^2} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {\log (x)}{x^2} \, dx,x,a+b x\right )}{b}\\ &=-\frac {1}{b (a+b x)}-\frac {\log (a+b x)}{b (a+b x)}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 21, normalized size = 0.68 \[ -\frac {\log (a+b x)+1}{a b+b^2 x} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.50, size = 21, normalized size = 0.68 \[ -\frac {\log \left (b x + a\right ) + 1}{b^{2} x + a b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, size = 32, normalized size = 1.03 \[ -b {\left (\frac {\log \left (b x + a\right )}{{\left (b x + a\right )} b^{2}} + \frac {1}{{\left (b x + a\right )} b^{2}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 32, normalized size = 1.03 \[ -\frac {\ln \left (b x +a \right )}{\left (b x +a \right ) b}-\frac {1}{\left (b x +a \right ) b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.67, size = 31, normalized size = 1.00 \[ -\frac {\log \left (b x + a\right )}{{\left (b x + a\right )} b} - \frac {1}{{\left (b x + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.49, size = 25, normalized size = 0.81 \[ -\frac {a+a\,\ln \left (a+b\,x\right )}{a\,b\,\left (a+b\,x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.20, size = 26, normalized size = 0.84 \[ - \frac {\log {\left (a + b x \right )}}{a b + b^{2} x} - \frac {1}{a b + b^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________