Optimal. Leaf size=52 \[ -\frac {2 (2+3 x)^{1+m}}{15 (1+m)}-\frac {11 (2+3 x)^{1+m} \, _2F_1(1,1+m;2+m;5 (2+3 x))}{5 (1+m)} \]
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Rubi [A]
time = 0.01, antiderivative size = 52, 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(1,m+1;m+2;5 (3 x+2))}{5 (m+1)}-\frac {2 (3 x+2)^{m+1}}{15 (m+1)} \end {gather*}
Antiderivative was successfully verified.
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Rule 70
Rule 81
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^m}{3+5 x} \, dx &=-\frac {2 (2+3 x)^{1+m}}{15 (1+m)}+\frac {11}{5} \int \frac {(2+3 x)^m}{3+5 x} \, dx\\ &=-\frac {2 (2+3 x)^{1+m}}{15 (1+m)}-\frac {11 (2+3 x)^{1+m} \, _2F_1(1,1+m;2+m;5 (2+3 x))}{5 (1+m)}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 37, normalized size = 0.71 \begin {gather*} -\frac {(2+3 x)^{1+m} (2+33 \, _2F_1(1,1+m;2+m;5 (2+3 x)))}{15 (1+m)} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (1-2 x \right ) \left (2+3 x \right )^{m}}{3+5 x}\, dx\]
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 \left (- \frac {\left (3 x + 2\right )^{m}}{5 x + 3}\right )\, dx - \int \frac {2 x \left (3 x + 2\right )^{m}}{5 x + 3}\, 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 (2\,x-1\right )\,{\left (3\,x+2\right )}^m}{5\,x+3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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