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, 245} \[ 6^m x \, _2F_1\left (\frac {1}{2},-m;\frac {3}{2};4 x^2\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 41
Rule 245
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 = 0.01, size = 20, normalized size = 1.00 \[ 6^m x \, _2F_1\left (\frac {1}{2},-m;\frac {3}{2};4 x^2\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (4 \, x + 2\right )}^{m} {\left (-6 \, x + 3\right )}^{m}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (4 \, x + 2\right )}^{m} {\left (-6 \, x + 3\right )}^{m}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.09, size = 0, normalized size = 0.00 \[ \int \left (4 x +2\right )^{m} \left (-6 x +3\right )^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (4 \, x + 2\right )}^{m} {\left (-6 \, x + 3\right )}^{m}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.05 \[ \int {\left (4\,x+2\right )}^m\,{\left (3-6\,x\right )}^m \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [C] time = 4.34, size = 42, normalized size = 2.10 \[ \frac {24^{m} \left (x + \frac {1}{2}\right ) \left (x + \frac {1}{2}\right )^{m} \Gamma \left (m + 1\right ) {{}_{2}F_{1}\left (\begin {matrix} - m, m + 1 \\ m + 2 \end {matrix}\middle | {\left (x + \frac {1}{2}\right ) e^{2 i \pi }} \right )}}{\Gamma \left (m + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________