Optimal. Leaf size=14 \[ -\frac{2}{b \sqrt{a+b x}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0013755, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {32} \[ -\frac{2}{b \sqrt{a+b x}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 32
Rubi steps
\begin{align*} \int \frac{1}{(a+b x)^{3/2}} \, dx &=-\frac{2}{b \sqrt{a+b x}}\\ \end{align*}
Mathematica [A] time = 0.0048989, size = 14, normalized size = 1. \[ -\frac{2}{b \sqrt{a+b x}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 13, normalized size = 0.9 \begin{align*} -2\,{\frac{1}{b\sqrt{bx+a}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.0712, size = 16, normalized size = 1.14 \begin{align*} -\frac{2}{\sqrt{b x + a} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.51328, size = 43, normalized size = 3.07 \begin{align*} -\frac{2 \, \sqrt{b x + a}}{b^{2} x + a b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.0651, size = 12, normalized size = 0.86 \begin{align*} - \frac{2}{b \sqrt{a + b x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.20343, size = 16, normalized size = 1.14 \begin{align*} -\frac{2}{\sqrt{b x + a} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]