Optimal. Leaf size=90 \[ -\frac {5135 (2+3 x)^{1+m}}{216 (1+m)}-\frac {725 (2+3 x)^{2+m}}{108 (2+m)}-\frac {125 (2+3 x)^{3+m}}{54 (3+m)}+\frac {1331 (2+3 x)^{1+m} \, _2F_1\left (1,1+m;2+m;\frac {2}{7} (2+3 x)\right )}{56 (1+m)} \]
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Rubi [A]
time = 0.02, 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 = {90, 70}
\begin {gather*} \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)} \end {gather*}
Antiderivative was successfully verified.
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Rule 70
Rule 90
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 = 0.11, size = 71, normalized size = 0.79 \begin {gather*} \frac {(2+3 x)^{1+m} \left (-\frac {35945}{1+m}-\frac {10150 (2+3 x)}{2+m}-\frac {3500 (2+3 x)^2}{3+m}+\frac {35937 \, _2F_1\left (1,1+m;2+m;\frac {2}{7} (2+3 x)\right )}{1+m}\right )}{1512} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (2+3 x \right )^{m} \left (3+5 x \right )^{3}}{1-2 x}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} - \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 \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int -\frac {{\left (3\,x+2\right )}^m\,{\left (5\,x+3\right )}^3}{2\,x-1} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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