Optimal. Leaf size=19 \[ -\frac {2 a}{\sqrt {x}}-\frac {2 b}{3 x^{3/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 19, 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 = {14} \[ -\frac {2 a}{\sqrt {x}}-\frac {2 b}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int \frac {a+\frac {b}{x}}{x^{3/2}} \, dx &=\int \left (\frac {b}{x^{5/2}}+\frac {a}{x^{3/2}}\right ) \, dx\\ &=-\frac {2 b}{3 x^{3/2}}-\frac {2 a}{\sqrt {x}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 15, normalized size = 0.79 \[ -\frac {2 (3 a x+b)}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.94, size = 11, normalized size = 0.58 \[ -\frac {2 \, {\left (3 \, a x + b\right )}}{3 \, x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 11, normalized size = 0.58 \[ -\frac {2 \, {\left (3 \, a x + b\right )}}{3 \, x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 12, normalized size = 0.63 \[ -\frac {2 \left (3 a x +b \right )}{3 x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.07, size = 13, normalized size = 0.68 \[ -\frac {2 \, a}{\sqrt {x}} - \frac {2 \, b}{3 \, x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 13, normalized size = 0.68 \[ -\frac {2\,b+6\,a\,x}{3\,x^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.50, size = 19, normalized size = 1.00 \[ - \frac {2 a}{\sqrt {x}} - \frac {2 b}{3 x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________