\(\int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx\) [1381]

Optimal result

Integrand size = 22, antiderivative size = 55 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx=\frac {2287 x}{729}-\frac {5287 x^2}{486}-\frac {190 x^3}{81}+\frac {775 x^4}{27}-\frac {200 x^5}{9}+\frac {343}{2187 (2+3 x)}+\frac {1813}{729} \log (2+3 x) \]

[Out]

2287/729*x-5287/486*x^2-190/81*x^3+775/27*x^4-200/9*x^5+343/2187/(2+3*x)+1813/729*ln(2+3*x)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx=-\frac {200 x^5}{9}+\frac {775 x^4}{27}-\frac {190 x^3}{81}-\frac {5287 x^2}{486}+\frac {2287 x}{729}+\frac {343}{2187 (3 x+2)}+\frac {1813}{729} \log (3 x+2) \]

[In]

Int[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^2,x]

[Out]

(2287*x)/729 - (5287*x^2)/486 - (190*x^3)/81 + (775*x^4)/27 - (200*x^5)/9 + 343/(2187*(2 + 3*x)) + (1813*Log[2
+ 3*x])/729

Rule 90

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {2287}{729}-\frac {5287 x}{243}-\frac {190 x^2}{27}+\frac {3100 x^3}{27}-\frac {1000 x^4}{9}-\frac {343}{729 (2+3 x)^2}+\frac {1813}{243 (2+3 x)}\right ) \, dx \\ & = \frac {2287 x}{729}-\frac {5287 x^2}{486}-\frac {190 x^3}{81}+\frac {775 x^4}{27}-\frac {200 x^5}{9}+\frac {343}{2187 (2+3 x)}+\frac {1813}{729} \log (2+3 x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx=-\frac {20002+3588 x+54000 x^2+163269 x^3-220320 x^4-182250 x^5+291600 x^6-10878 (2+3 x) \log (2+3 x)}{4374 (2+3 x)} \]

[In]

Integrate[((1 - 2*x)^3*(3 + 5*x)^3)/(2 + 3*x)^2,x]

[Out]

-1/4374*(20002 + 3588*x + 54000*x^2 + 163269*x^3 - 220320*x^4 - 182250*x^5 + 291600*x^6 - 10878*(2 + 3*x)*Log[
2 + 3*x])/(2 + 3*x)

Maple [A] (verified)

Time = 2.43 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.73

method	result	size
risch	\(-\frac {200 x^{5}}{9}+\frac {775 x^{4}}{27}-\frac {190 x^{3}}{81}-\frac {5287 x^{2}}{486}+\frac {2287 x}{729}+\frac {343}{6561 \left (\frac {2}{3}+x \right )}+\frac {1813 \ln \left (2+3 x \right )}{729}\)	\(40\)
default	\(\frac {2287 x}{729}-\frac {5287 x^{2}}{486}-\frac {190 x^{3}}{81}+\frac {775 x^{4}}{27}-\frac {200 x^{5}}{9}+\frac {343}{2187 \left (2+3 x \right )}+\frac {1813 \ln \left (2+3 x \right )}{729}\)	\(42\)
norman	\(\frac {\frac {2935}{486} x -\frac {1000}{81} x^{2}-\frac {6047}{162} x^{3}+\frac {1360}{27} x^{4}+\frac {125}{3} x^{5}-\frac {200}{3} x^{6}}{2+3 x}+\frac {1813 \ln \left (2+3 x \right )}{729}\)	\(47\)
parallelrisch	\(\frac {-97200 x^{6}+60750 x^{5}+73440 x^{4}-54423 x^{3}+10878 \ln \left (\frac {2}{3}+x \right ) x -18000 x^{2}+7252 \ln \left (\frac {2}{3}+x \right )+8805 x}{2916+4374 x}\)	\(52\)
meijerg	\(\frac {45 x}{4 \left (1+\frac {3 x}{2}\right )}+\frac {1813 \ln \left (1+\frac {3 x}{2}\right )}{729}-\frac {29 x \left (\frac {9 x}{2}+6\right )}{3 \left (1+\frac {3 x}{2}\right )}-\frac {179 x \left (-\frac {9}{2} x^{2}+9 x +12\right )}{54 \left (1+\frac {3 x}{2}\right )}+\frac {232 x \left (\frac {135}{8} x^{3}-\frac {45}{2} x^{2}+45 x +60\right )}{81 \left (1+\frac {3 x}{2}\right )}+\frac {200 x \left (-\frac {243}{16} x^{4}+\frac {135}{8} x^{3}-\frac {45}{2} x^{2}+45 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )}-\frac {1600 x \left (\frac {1701}{16} x^{5}-\frac {1701}{16} x^{4}+\frac {945}{8} x^{3}-\frac {315}{2} x^{2}+315 x +420\right )}{5103 \left (1+\frac {3 x}{2}\right )}\)	\(145\)

[In]

int((1-2*x)^3*(3+5*x)^3/(2+3*x)^2,x,method=_RETURNVERBOSE)

[Out]

-200/9*x^5+775/27*x^4-190/81*x^3-5287/486*x^2+2287/729*x+343/6561/(2/3+x)+1813/729*ln(2+3*x)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.95 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx=-\frac {291600 \, x^{6} - 182250 \, x^{5} - 220320 \, x^{4} + 163269 \, x^{3} + 54000 \, x^{2} - 10878 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 27444 \, x - 686}{4374 \, {\left (3 \, x + 2\right )}} \]

[In]

integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^2,x, algorithm="fricas")

[Out]

-1/4374*(291600*x^6 - 182250*x^5 - 220320*x^4 + 163269*x^3 + 54000*x^2 - 10878*(3*x + 2)*log(3*x + 2) - 27444*
x - 686)/(3*x + 2)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.87 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx=- \frac {200 x^{5}}{9} + \frac {775 x^{4}}{27} - \frac {190 x^{3}}{81} - \frac {5287 x^{2}}{486} + \frac {2287 x}{729} + \frac {1813 \log {\left (3 x + 2 \right )}}{729} + \frac {343}{6561 x + 4374} \]

[In]

integrate((1-2*x)**3*(3+5*x)**3/(2+3*x)**2,x)

[Out]

-200*x**5/9 + 775*x**4/27 - 190*x**3/81 - 5287*x**2/486 + 2287*x/729 + 1813*log(3*x + 2)/729 + 343/(6561*x + 4
374)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.75 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx=-\frac {200}{9} \, x^{5} + \frac {775}{27} \, x^{4} - \frac {190}{81} \, x^{3} - \frac {5287}{486} \, x^{2} + \frac {2287}{729} \, x + \frac {343}{2187 \, {\left (3 \, x + 2\right )}} + \frac {1813}{729} \, \log \left (3 \, x + 2\right ) \]

[In]

integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^2,x, algorithm="maxima")

[Out]

-200/9*x^5 + 775/27*x^4 - 190/81*x^3 - 5287/486*x^2 + 2287/729*x + 343/2187/(3*x + 2) + 1813/729*log(3*x + 2)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.36 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx=\frac {1}{4374} \, {\left (3 \, x + 2\right )}^{5} {\left (\frac {5550}{3 \, x + 2} - \frac {28780}{{\left (3 \, x + 2\right )}^{2}} + \frac {66193}{{\left (3 \, x + 2\right )}^{3}} - \frac {60438}{{\left (3 \, x + 2\right )}^{4}} - 400\right )} + \frac {343}{2187 \, {\left (3 \, x + 2\right )}} - \frac {1813}{729} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \]

[In]

integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^2,x, algorithm="giac")

[Out]

1/4374*(3*x + 2)^5*(5550/(3*x + 2) - 28780/(3*x + 2)^2 + 66193/(3*x + 2)^3 - 60438/(3*x + 2)^4 - 400) + 343/21
87/(3*x + 2) - 1813/729*log(1/3*abs(3*x + 2)/(3*x + 2)^2)

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^2} \, dx=\frac {2287\,x}{729}+\frac {1813\,\ln \left (x+\frac {2}{3}\right )}{729}+\frac {343}{6561\,\left (x+\frac {2}{3}\right )}-\frac {5287\,x^2}{486}-\frac {190\,x^3}{81}+\frac {775\,x^4}{27}-\frac {200\,x^5}{9} \]

[In]

int(-((2*x - 1)^3*(5*x + 3)^3)/(3*x + 2)^2,x)

[Out]

(2287*x)/729 + (1813*log(x + 2/3))/729 + 343/(6561*(x + 2/3)) - (5287*x^2)/486 - (190*x^3)/81 + (775*x^4)/27 -
(200*x^5)/9