Optimal. Leaf size=10 \[ \frac {\log (a+b x)}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {31}
\begin {gather*} \frac {\log (a+b x)}{b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rubi steps
\begin {align*} \int \frac {1}{a+b x} \, dx &=\frac {\log (a+b x)}{b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {\log (a+b x)}{b} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 11, normalized size = 1.10
method | result | size |
default | \(\frac {\ln \left (b x +a \right )}{b}\) | \(11\) |
norman | \(\frac {\ln \left (b x +a \right )}{b}\) | \(11\) |
risch | \(\frac {\ln \left (b x +a \right )}{b}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 10, normalized size = 1.00 \begin {gather*} \frac {\log \left (b x + a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.18, size = 10, normalized size = 1.00 \begin {gather*} \frac {\log \left (b x + a\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 7, normalized size = 0.70 \begin {gather*} \frac {\log {\left (a + b x \right )}}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.16, size = 11, normalized size = 1.10 \begin {gather*} \frac {\log \left ({\left | b x + a \right |}\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 10, normalized size = 1.00 \begin {gather*} \frac {\ln \left (a+b\,x\right )}{b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________