Optimal. Leaf size=54 \[ \frac{11 (3 x+2)^{m+1} \, _2F_1\left (1,m+1;m+2;\frac{2}{7} (3 x+2)\right )}{14 (m+1)}-\frac{5 (3 x+2)^{m+1}}{6 (m+1)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0471738, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{11 (3 x+2)^{m+1} \, _2F_1\left (1,m+1;m+2;\frac{2}{7} (3 x+2)\right )}{14 (m+1)}-\frac{5 (3 x+2)^{m+1}}{6 (m+1)} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^m*(3 + 5*x))/(1 - 2*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.47515, size = 42, normalized size = 0.78 \[ \frac{11 \left (3 x + 2\right )^{m + 1}{{}_{2}F_{1}\left (\begin{matrix} 1, m + 1 \\ m + 2 \end{matrix}\middle |{\frac{6 x}{7} + \frac{4}{7}} \right )}}{14 \left (m + 1\right )} - \frac{5 \left (3 x + 2\right )^{m + 1}}{6 \left (m + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**m*(3+5*x)/(1-2*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.112026, size = 67, normalized size = 1.24 \[ \frac{1}{12} (3 x+2)^m \left (-\frac{33 \left (\frac{6 x+4}{6 x-3}\right )^{-m} \, _2F_1\left (-m,-m;1-m;\frac{7}{3-6 x}\right )}{m}-\frac{10 (3 x+2)}{m+1}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^m*(3 + 5*x))/(1 - 2*x),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.054, size = 0, normalized size = 0. \[ \int{\frac{ \left ( 2+3\,x \right ) ^{m} \left ( 3+5\,x \right ) }{1-2\,x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^m*(3+5*x)/(1-2*x),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ -\int \frac{{\left (3 \, x + 2\right )}^{m}{\left (5 \, x + 3\right )}}{2 \, x - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^m*(5*x + 3)/(2*x - 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (-\frac{{\left (3 \, x + 2\right )}^{m}{\left (5 \, x + 3\right )}}{2 \, x - 1}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^m*(5*x + 3)/(2*x - 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \int \frac{3 \left (3 x + 2\right )^{m}}{2 x - 1}\, dx - \int \frac{5 x \left (3 x + 2\right )^{m}}{2 x - 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**m*(3+5*x)/(1-2*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int -\frac{{\left (3 \, x + 2\right )}^{m}{\left (5 \, x + 3\right )}}{2 \, x - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^m*(5*x + 3)/(2*x - 1),x, algorithm="giac")
[Out]