Optimal. Leaf size=21 \[ \frac {\log \left (1-(-a)^{3/2} x\right )}{\sqrt {-a}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {31} \[ \frac {\log \left (1-(-a)^{3/2} x\right )}{\sqrt {-a}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rubi steps
\begin {align*} \int \frac {1}{\frac {1}{a}+\sqrt {-a} x} \, dx &=\frac {\log \left (1-(-a)^{3/2} x\right )}{\sqrt {-a}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ \frac {\log \left (\sqrt {-a} a x+1\right )}{\sqrt {-a}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.49, size = 24, normalized size = 1.14 \[ -\frac {\sqrt {-a} \log \left (a^{2} x - \sqrt {-a}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.04, size = 19, normalized size = 0.90 \[ \frac {\log \left ({\left | \sqrt {-a} x + \frac {1}{a} \right |}\right )}{\sqrt {-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 19, normalized size = 0.90 \[ \frac {\ln \left (\sqrt {-a}\, x +\frac {1}{a}\right )}{\sqrt {-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.33, size = 18, normalized size = 0.86 \[ \frac {\log \left (\sqrt {-a} x + \frac {1}{a}\right )}{\sqrt {-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.15, size = 16, normalized size = 0.76 \[ \frac {\ln \left (x-\frac {1}{{\left (-a\right )}^{3/2}}\right )}{\sqrt {-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 19, normalized size = 0.90 \[ \frac {\log {\left (a x \sqrt {- a} + 1 \right )}}{\sqrt {- a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________