Optimal. Leaf size=55 \[ \frac {29 (5 x+3)^4}{36 (3 x+2)^4}+\frac {29 (5 x+3)^4}{45 (3 x+2)^5}+\frac {7 (5 x+3)^4}{18 (3 x+2)^6} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {78, 45, 37} \begin {gather*} \frac {29 (5 x+3)^4}{36 (3 x+2)^4}+\frac {29 (5 x+3)^4}{45 (3 x+2)^5}+\frac {7 (5 x+3)^4}{18 (3 x+2)^6} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rule 45
Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^7} \, dx &=\frac {7 (3+5 x)^4}{18 (2+3 x)^6}+\frac {29}{9} \int \frac {(3+5 x)^3}{(2+3 x)^6} \, dx\\ &=\frac {7 (3+5 x)^4}{18 (2+3 x)^6}+\frac {29 (3+5 x)^4}{45 (2+3 x)^5}+\frac {29}{9} \int \frac {(3+5 x)^3}{(2+3 x)^5} \, dx\\ &=\frac {7 (3+5 x)^4}{18 (2+3 x)^6}+\frac {29 (3+5 x)^4}{45 (2+3 x)^5}+\frac {29 (3+5 x)^4}{36 (2+3 x)^4}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 31, normalized size = 0.56 \begin {gather*} \frac {607500 x^4+1066500 x^3+587925 x^2+78048 x-13198}{14580 (3 x+2)^6} \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)^3}{(2+3 x)^7} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.22, size = 54, normalized size = 0.98 \begin {gather*} \frac {607500 \, x^{4} + 1066500 \, x^{3} + 587925 \, x^{2} + 78048 \, x - 13198}{14580 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.18, size = 29, normalized size = 0.53 \begin {gather*} \frac {607500 \, x^{4} + 1066500 \, x^{3} + 587925 \, x^{2} + 78048 \, x - 13198}{14580 \, {\left (3 \, x + 2\right )}^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 47, normalized size = 0.85 \begin {gather*} \frac {7}{1458 \left (3 x +2\right )^{6}}-\frac {1025}{729 \left (3 x +2\right )^{3}}+\frac {185}{324 \left (3 x +2\right )^{4}}+\frac {125}{243 \left (3 x +2\right )^{2}}-\frac {107}{1215 \left (3 x +2\right )^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.55, size = 54, normalized size = 0.98 \begin {gather*} \frac {607500 \, x^{4} + 1066500 \, x^{3} + 587925 \, x^{2} + 78048 \, x - 13198}{14580 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 46, normalized size = 0.84 \begin {gather*} \frac {125}{243\,{\left (3\,x+2\right )}^2}-\frac {1025}{729\,{\left (3\,x+2\right )}^3}+\frac {185}{324\,{\left (3\,x+2\right )}^4}-\frac {107}{1215\,{\left (3\,x+2\right )}^5}+\frac {7}{1458\,{\left (3\,x+2\right )}^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 51, normalized size = 0.93 \begin {gather*} - \frac {- 607500 x^{4} - 1066500 x^{3} - 587925 x^{2} - 78048 x + 13198}{10628820 x^{6} + 42515280 x^{5} + 70858800 x^{4} + 62985600 x^{3} + 31492800 x^{2} + 8398080 x + 933120} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________