Optimal. Leaf size=20 \[ \frac {\log \left (\sqrt {-a} x+a\right )}{\sqrt {-a}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {31} \[ \frac {\log \left (\sqrt {-a} x+a\right )}{\sqrt {-a}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rubi steps
\begin {align*} \int \frac {1}{a+\sqrt {-a} x} \, dx &=\frac {\log \left (a+\sqrt {-a} x\right )}{\sqrt {-a}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \[ \frac {\log \left (\sqrt {-a} x+a\right )}{\sqrt {-a}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.49, size = 20, normalized size = 1.00 \[ -\frac {\sqrt {-a} \log \left (x - \sqrt {-a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.10, size = 17, normalized size = 0.85 \[ \frac {\log \left ({\left | \sqrt {-a} x + a \right |}\right )}{\sqrt {-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 17, normalized size = 0.85 \[ \frac {\ln \left (a +\sqrt {-a}\, x \right )}{\sqrt {-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.37, size = 16, normalized size = 0.80 \[ \frac {\log \left (\sqrt {-a} x + a\right )}{\sqrt {-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.11, size = 16, normalized size = 0.80 \[ \frac {\ln \left (x-\sqrt {-a}\right )}{\sqrt {-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 17, normalized size = 0.85 \[ \frac {\log {\left (a + x \sqrt {- a} \right )}}{\sqrt {- a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________