Optimal. Leaf size=90 \[ \frac {1331 (3 x+2)^{m+1} \, _2F_1\left (1,m+1;m+2;\frac {2}{7} (3 x+2)\right )}{56 (m+1)}-\frac {5135 (3 x+2)^{m+1}}{216 (m+1)}-\frac {725 (3 x+2)^{m+2}}{108 (m+2)}-\frac {125 (3 x+2)^{m+3}}{54 (m+3)} \]
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Rubi [A] time = 0.03, antiderivative size = 90, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {88, 68} \[ \frac {1331 (3 x+2)^{m+1} \, _2F_1\left (1,m+1;m+2;\frac {2}{7} (3 x+2)\right )}{56 (m+1)}-\frac {5135 (3 x+2)^{m+1}}{216 (m+1)}-\frac {725 (3 x+2)^{m+2}}{108 (m+2)}-\frac {125 (3 x+2)^{m+3}}{54 (m+3)} \]
Antiderivative was successfully verified.
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Rule 68
Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^m (3+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac {5135}{72} (2+3 x)^m+\frac {1331 (2+3 x)^m}{8 (1-2 x)}-\frac {725}{36} (2+3 x)^{1+m}-\frac {125}{18} (2+3 x)^{2+m}\right ) \, dx\\ &=-\frac {5135 (2+3 x)^{1+m}}{216 (1+m)}-\frac {725 (2+3 x)^{2+m}}{108 (2+m)}-\frac {125 (2+3 x)^{3+m}}{54 (3+m)}+\frac {1331}{8} \int \frac {(2+3 x)^m}{1-2 x} \, dx\\ &=-\frac {5135 (2+3 x)^{1+m}}{216 (1+m)}-\frac {725 (2+3 x)^{2+m}}{108 (2+m)}-\frac {125 (2+3 x)^{3+m}}{54 (3+m)}+\frac {1331 (2+3 x)^{1+m} \, _2F_1\left (1,1+m;2+m;\frac {2}{7} (2+3 x)\right )}{56 (1+m)}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 71, normalized size = 0.79 \[ \frac {(3 x+2)^{m+1} \left (\frac {35937 \, _2F_1\left (1,m+1;m+2;\frac {2}{7} (3 x+2)\right )}{m+1}-\frac {3500 (3 x+2)^2}{m+3}-\frac {10150 (3 x+2)}{m+2}-\frac {35945}{m+1}\right )}{1512} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.71, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {{\left (125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27\right )} {\left (3 \, x + 2\right )}^{m}}{2 \, x - 1}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int -\frac {{\left (3 \, x + 2\right )}^{m} {\left (5 \, x + 3\right )}^{3}}{2 \, x - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.24, size = 0, normalized size = 0.00 \[ \int \frac {\left (5 x +3\right )^{3} \left (3 x +2\right )^{m}}{-2 x +1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ -\int \frac {{\left (3 \, x + 2\right )}^{m} {\left (5 \, x + 3\right )}^{3}}{2 \, x - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \[ \int -\frac {{\left (3\,x+2\right )}^m\,{\left (5\,x+3\right )}^3}{2\,x-1} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ - \int \frac {27 \left (3 x + 2\right )^{m}}{2 x - 1}\, dx - \int \frac {135 x \left (3 x + 2\right )^{m}}{2 x - 1}\, dx - \int \frac {225 x^{2} \left (3 x + 2\right )^{m}}{2 x - 1}\, dx - \int \frac {125 x^{3} \left (3 x + 2\right )^{m}}{2 x - 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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