Optimal. Leaf size=19 \[ 2 a \sqrt {x}+\frac {2}{9} c x^{9/2} \]
[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}
\begin {gather*} 2 a \sqrt {x}+\frac {2}{9} c x^{9/2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int \frac {a+c x^4}{\sqrt {x}} \, dx &=\int \left (\frac {a}{\sqrt {x}}+c x^{7/2}\right ) \, dx\\ &=2 a \sqrt {x}+\frac {2}{9} c x^{9/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 20, normalized size = 1.05 \begin {gather*} \frac {2}{9} \left (9 a \sqrt {x}+c x^{9/2}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 14, normalized size = 0.74
method | result | size |
derivativedivides | \(\frac {2 c \,x^{\frac {9}{2}}}{9}+2 a \sqrt {x}\) | \(14\) |
default | \(\frac {2 c \,x^{\frac {9}{2}}}{9}+2 a \sqrt {x}\) | \(14\) |
gosper | \(\frac {2 \sqrt {x}\, \left (x^{4} c +9 a \right )}{9}\) | \(15\) |
trager | \(\left (\frac {2 x^{4} c}{9}+2 a \right ) \sqrt {x}\) | \(15\) |
risch | \(\frac {2 \sqrt {x}\, \left (x^{4} c +9 a \right )}{9}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{9} \, c x^{\frac {9}{2}} + 2 \, a \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 14, normalized size = 0.74 \begin {gather*} \frac {2}{9} \, {\left (c x^{4} + 9 \, a\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.14, size = 17, normalized size = 0.89 \begin {gather*} 2 a \sqrt {x} + \frac {2 c x^{\frac {9}{2}}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.72, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{9} \, c x^{\frac {9}{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 = 14, normalized size = 0.74 \begin {gather*} \frac {2\,\sqrt {x}\,\left (c\,x^4+9\,a\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________