Optimal. Leaf size=45 \[ \frac {25}{162 (3 x+2)^4}-\frac {13}{27 (3 x+2)^5}+\frac {4}{27 (3 x+2)^6}-\frac {1}{81 (3 x+2)^7} \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} \frac {25}{162 (3 x+2)^4}-\frac {13}{27 (3 x+2)^5}+\frac {4}{27 (3 x+2)^6}-\frac {1}{81 (3 x+2)^7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^8} \, dx &=\int \left (\frac {7}{27 (2+3 x)^8}-\frac {8}{3 (2+3 x)^7}+\frac {65}{9 (2+3 x)^6}-\frac {50}{27 (2+3 x)^5}\right ) \, dx\\ &=-\frac {1}{81 (2+3 x)^7}+\frac {4}{27 (2+3 x)^6}-\frac {13}{27 (2+3 x)^5}+\frac {25}{162 (2+3 x)^4}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 26, normalized size = 0.58 \begin {gather*} \frac {225 x^3+216 x^2+12 x-22}{54 (3 x+2)^7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^8} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.21, size = 54, normalized size = 1.20 \begin {gather*} \frac {225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.21, size = 24, normalized size = 0.53 \begin {gather*} \frac {225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \, {\left (3 \, x + 2\right )}^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 38, normalized size = 0.84 \begin {gather*} -\frac {1}{81 \left (3 x +2\right )^{7}}+\frac {4}{27 \left (3 x +2\right )^{6}}-\frac {13}{27 \left (3 x +2\right )^{5}}+\frac {25}{162 \left (3 x +2\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.53, size = 54, normalized size = 1.20 \begin {gather*} \frac {225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.11, size = 37, normalized size = 0.82 \begin {gather*} \frac {25}{162\,{\left (3\,x+2\right )}^4}-\frac {13}{27\,{\left (3\,x+2\right )}^5}+\frac {4}{27\,{\left (3\,x+2\right )}^6}-\frac {1}{81\,{\left (3\,x+2\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 51, normalized size = 1.13 \begin {gather*} - \frac {- 225 x^{3} - 216 x^{2} - 12 x + 22}{118098 x^{7} + 551124 x^{6} + 1102248 x^{5} + 1224720 x^{4} + 816480 x^{3} + 326592 x^{2} + 72576 x + 6912} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________