Optimal. Leaf size=20 \[ 6^m x \, _2F_1\left (\frac {1}{2},-m;\frac {3}{2};4 x^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {41, 251}
\begin {gather*} 6^m x \, _2F_1\left (\frac {1}{2},-m;\frac {3}{2};4 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 41
Rule 251
Rubi steps
\begin {align*} \int (3-6 x)^m (2+4 x)^m \, dx &=\int \left (6-24 x^2\right )^m \, dx\\ &=6^m x \, _2F_1\left (\frac {1}{2},-m;\frac {3}{2};4 x^2\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 20, normalized size = 1.00 \begin {gather*} 6^m x \, _2F_1\left (\frac {1}{2},-m;\frac {3}{2};4 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.06, size = 0, normalized size = 0.00 \[\int \left (3-6 x \right )^{m} \left (2+4 x \right )^{m}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [C] Result contains complex when optimal does not.
time = 2.22, size = 42, normalized size = 2.10 \begin {gather*} \frac {24^{m} \left (x + \frac {1}{2}\right ) \left (x + \frac {1}{2}\right )^{m} \Gamma \left (m + 1\right ) {{}_{2}F_{1}\left (\begin {matrix} - m, m + 1 \\ m + 2 \end {matrix}\middle | {\left (x + \frac {1}{2}\right ) e^{2 i \pi }} \right )}}{\Gamma \left (m + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int {\left (4\,x+2\right )}^m\,{\left (3-6\,x\right )}^m \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________