Optimal. Leaf size=31 \[ \frac {2}{7} a x^{7/2}+\frac {2}{11} b x^{11/2}+\frac {2}{15} c x^{15/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \[ \frac {2}{7} a x^{7/2}+\frac {2}{11} b x^{11/2}+\frac {2}{15} c x^{15/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int x^{5/2} \left (a+b x^2+c x^4\right ) \, dx &=\int \left (a x^{5/2}+b x^{9/2}+c x^{13/2}\right ) \, dx\\ &=\frac {2}{7} a x^{7/2}+\frac {2}{11} b x^{11/2}+\frac {2}{15} c x^{15/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 25, normalized size = 0.81 \[ \frac {2 x^{7/2} \left (165 a+105 b x^2+77 c x^4\right )}{1155} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.75, size = 24, normalized size = 0.77 \[ \frac {2}{1155} \, {\left (77 \, c x^{7} + 105 \, b x^{5} + 165 \, a x^{3}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 19, normalized size = 0.61 \[ \frac {2}{15} \, c x^{\frac {15}{2}} + \frac {2}{11} \, b x^{\frac {11}{2}} + \frac {2}{7} \, a x^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 22, normalized size = 0.71 \[ \frac {2 \left (77 c \,x^{4}+105 b \,x^{2}+165 a \right ) x^{\frac {7}{2}}}{1155} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.98, size = 19, normalized size = 0.61 \[ \frac {2}{15} \, c x^{\frac {15}{2}} + \frac {2}{11} \, b x^{\frac {11}{2}} + \frac {2}{7} \, a x^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.29, size = 21, normalized size = 0.68 \[ \frac {2\,x^{7/2}\,\left (77\,c\,x^4+105\,b\,x^2+165\,a\right )}{1155} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 6.72, size = 29, normalized size = 0.94 \[ \frac {2 a x^{\frac {7}{2}}}{7} + \frac {2 b x^{\frac {11}{2}}}{11} + \frac {2 c x^{\frac {15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________