Optimal. Leaf size=17 \[ 2 b \sqrt {x}-\frac {2 a}{\sqrt {x}} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \begin {gather*} 2 b \sqrt {x}-\frac {2 a}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^{3/2}} \, dx &=\int \left (\frac {a}{x^{3/2}}+\frac {b}{\sqrt {x}}\right ) \, dx\\ &=-\frac {2 a}{\sqrt {x}}+2 b \sqrt {x}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 14, normalized size = 0.82 \begin {gather*} \frac {2 (b x-a)}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.01, size = 14, normalized size = 0.82 \begin {gather*} \frac {2 (b x-a)}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.55, size = 12, normalized size = 0.71 \begin {gather*} \frac {2 \, {\left (b x - a\right )}}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.92, size = 13, normalized size = 0.76 \begin {gather*} 2 \, b \sqrt {x} - \frac {2 \, a}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 12, normalized size = 0.71 \begin {gather*} -\frac {2 \left (-b x +a \right )}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.33, size = 13, normalized size = 0.76 \begin {gather*} 2 \, b \sqrt {x} - \frac {2 \, a}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 11, normalized size = 0.65 \begin {gather*} -\frac {2\,\left (a-b\,x\right )}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.35, size = 15, normalized size = 0.88 \begin {gather*} - \frac {2 a}{\sqrt {x}} + 2 b \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________