Optimal. Leaf size=19 \[ 2 a \sqrt {x}+\frac {2}{3} b x^{3/2} \]
[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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} 2 a \sqrt {x}+\frac {2}{3} b x^{3/2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rubi steps
\begin {align*} \int \frac {a+b x}{\sqrt {x}} \, dx &=\int \left (\frac {a}{\sqrt {x}}+b \sqrt {x}\right ) \, dx\\ &=2 a \sqrt {x}+\frac {2}{3} b x^{3/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 16, normalized size = 0.84 \begin {gather*} \frac {2}{3} \sqrt {x} (3 a+b x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 14, normalized size = 0.74
method | result | size |
gosper | \(\frac {2 \sqrt {x}\, \left (b x +3 a \right )}{3}\) | \(13\) |
trager | \(\left (\frac {2 b x}{3}+2 a \right ) \sqrt {x}\) | \(13\) |
risch | \(\frac {2 \sqrt {x}\, \left (b x +3 a \right )}{3}\) | \(13\) |
derivativedivides | \(\frac {2 b \,x^{\frac {3}{2}}}{3}+2 a \sqrt {x}\) | \(14\) |
default | \(\frac {2 b \,x^{\frac {3}{2}}}{3}+2 a \sqrt {x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{3} \, b x^{\frac {3}{2}} + 2 \, a \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.46, size = 12, normalized size = 0.63 \begin {gather*} \frac {2}{3} \, {\left (b x + 3 \, a\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 17, normalized size = 0.89 \begin {gather*} 2 a \sqrt {x} + \frac {2 b x^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.92, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{3} \, b x^{\frac {3}{2}} + 2 \, a \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 12, normalized size = 0.63 \begin {gather*} \frac {2\,\sqrt {x}\,\left (3\,a+b\,x\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________