Optimal. Leaf size=54 \[ -\frac {5 (2+3 x)^{1+m}}{6 (1+m)}+\frac {11 (2+3 x)^{1+m} \, _2F_1\left (1,1+m;2+m;\frac {2}{7} (2+3 x)\right )}{14 (1+m)} \]
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Rubi [A]
time = 0.01, antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {81, 70}
\begin {gather*} \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)} \end {gather*}
Antiderivative was successfully verified.
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Rule 70
Rule 81
Rubi steps
\begin {align*} \int \frac {(2+3 x)^m (3+5 x)}{1-2 x} \, dx &=-\frac {5 (2+3 x)^{1+m}}{6 (1+m)}+\frac {11}{2} \int \frac {(2+3 x)^m}{1-2 x} \, dx\\ &=-\frac {5 (2+3 x)^{1+m}}{6 (1+m)}+\frac {11 (2+3 x)^{1+m} \, _2F_1\left (1,1+m;2+m;\frac {2}{7} (2+3 x)\right )}{14 (1+m)}\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 39, normalized size = 0.72 \begin {gather*} \frac {(2+3 x)^{1+m} \left (-35+33 \, _2F_1\left (1,1+m;2+m;\frac {2}{7} (2+3 x)\right )\right )}{42 (1+m)} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (2+3 x \right )^{m} \left (3+5 x \right )}{1-2 x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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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 {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 \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 = -0.02 \begin {gather*} \int -\frac {{\left (3\,x+2\right )}^m\,\left (5\,x+3\right )}{2\,x-1} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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