Optimal. Leaf size=59 \[ -\frac {11 (2+3 x)^{1+m}}{10 (3+5 x)^2}-\frac {3 (37-33 m) (2+3 x)^{1+m} \, _2F_1(2,1+m;2+m;5 (2+3 x))}{10 (1+m)} \]
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Rubi [A]
time = 0.02, antiderivative size = 59, 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 = {79, 70}
\begin {gather*} -\frac {3 (37-33 m) (3 x+2)^{m+1} \, _2F_1(2,m+1;m+2;5 (3 x+2))}{10 (m+1)}-\frac {11 (3 x+2)^{m+1}}{10 (5 x+3)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 70
Rule 79
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^m}{(3+5 x)^3} \, dx &=-\frac {11 (2+3 x)^{1+m}}{10 (3+5 x)^2}-\frac {1}{10} (37-33 m) \int \frac {(2+3 x)^m}{(3+5 x)^2} \, dx\\ &=-\frac {11 (2+3 x)^{1+m}}{10 (3+5 x)^2}-\frac {3 (37-33 m) (2+3 x)^{1+m} \, _2F_1(2,1+m;2+m;5 (2+3 x))}{10 (1+m)}\\ \end {align*}
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Mathematica [A]
time = 0.08, size = 48, normalized size = 0.81 \begin {gather*} \frac {1}{10} (2+3 x)^{1+m} \left (-\frac {11}{(3+5 x)^2}+\frac {3 (-37+33 m) \, _2F_1(2,1+m;2+m;10+15 x)}{1+m}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (1-2 x \right ) \left (2+3 x \right )^{m}}{\left (3+5 x \right )^{3}}\, dx\]
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}}{125 x^{3} + 225 x^{2} + 135 x + 27}\right )\, dx - \int \frac {2 x \left (3 x + 2\right )^{m}}{125 x^{3} + 225 x^{2} + 135 x + 27}\, 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}{{\left (5\,x+3\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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