Optimal. Leaf size=14 \[ \frac {1}{6} x^5 \sqrt {x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {15, 30} \[ \frac {1}{6} x^5 \sqrt {x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (x^2\right )^{5/2} \, dx &=\frac {\sqrt {x^2} \int x^5 \, dx}{x}\\ &=\frac {1}{6} x^5 \sqrt {x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 12, normalized size = 0.86 \[ \frac {1}{6} x \left (x^2\right )^{5/2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 5, normalized size = 0.36 \[ \frac {1}{6} \, x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 7, normalized size = 0.50 \[ \frac {1}{6} \, x^{6} \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 9, normalized size = 0.64 \[ \frac {\left (x^{2}\right )^{\frac {5}{2}} x}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.26, size = 8, normalized size = 0.57 \[ \frac {1}{6} \, {\left (x^{2}\right )}^{\frac {5}{2}} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.07 \[ \int {\left (x^2\right )}^{5/2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 3, normalized size = 0.21 \[ \frac {x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________