Optimal. Leaf size=10 \[ x-2 \log (3+2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {45}
\begin {gather*} x-2 \log (2 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rubi steps
\begin {align*} \int \frac {-1+2 x}{3+2 x} \, dx &=\int \left (1-\frac {4}{3+2 x}\right ) \, dx\\ &=x-2 \log (3+2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} x-2 \log (3+2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.05, size = 11, normalized size = 1.10
method | result | size |
default | \(x -2 \ln \left (3+2 x \right )\) | \(11\) |
norman | \(x -2 \ln \left (3+2 x \right )\) | \(11\) |
meijerg | \(-2 \ln \left (1+\frac {2 x}{3}\right )+x\) | \(11\) |
risch | \(x -2 \ln \left (3+2 x \right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 2.09, size = 10, normalized size = 1.00 \begin {gather*} x - 2 \, \log \left (2 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.71, size = 10, normalized size = 1.00 \begin {gather*} x - 2 \, \log \left (2 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 8, normalized size = 0.80 \begin {gather*} x - 2 \log {\left (2 x + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.77, size = 11, normalized size = 1.10 \begin {gather*} x - 2 \, \log \left ({\left | 2 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.06, size = 8, normalized size = 0.80 \begin {gather*} x-2\,\ln \left (x+\frac {3}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________