\(\int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx\) [1382]

Optimal result

Integrand size = 22, antiderivative size = 59 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx=\frac {16253 x}{729}-\frac {1795 x^2}{81}+\frac {1700 x^3}{81}-\frac {250 x^4}{27}+\frac {343}{4374 (2+3 x)^2}-\frac {1813}{729 (2+3 x)}-\frac {10073}{729} \log (2+3 x) \]

[Out]

16253/729*x-1795/81*x^2+1700/81*x^3-250/27*x^4+343/4374/(2+3*x)^2-1813/729/(2+3*x)-10073/729*ln(2+3*x)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 59, 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} \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx=-\frac {250 x^4}{27}+\frac {1700 x^3}{81}-\frac {1795 x^2}{81}+\frac {16253 x}{729}-\frac {1813}{729 (3 x+2)}+\frac {343}{4374 (3 x+2)^2}-\frac {10073}{729} \log (3 x+2) \]

[In]

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

[Out]

(16253*x)/729 - (1795*x^2)/81 + (1700*x^3)/81 - (250*x^4)/27 + 343/(4374*(2 + 3*x)^2) - 1813/(729*(2 + 3*x)) -
(10073*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 {16253}{729}-\frac {3590 x}{81}+\frac {1700 x^2}{27}-\frac {1000 x^3}{27}-\frac {343}{729 (2+3 x)^3}+\frac {1813}{243 (2+3 x)^2}-\frac {10073}{243 (2+3 x)}\right ) \, dx \\ & = \frac {16253 x}{729}-\frac {1795 x^2}{81}+\frac {1700 x^3}{81}-\frac {250 x^4}{27}+\frac {343}{4374 (2+3 x)^2}-\frac {1813}{729 (2+3 x)}-\frac {10073}{729} \log (2+3 x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.95 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx=\frac {551755+2076942 x+2072124 x^2+81702 x^3+67230 x^4+340200 x^5-364500 x^6-60438 (2+3 x)^2 \log (2+3 x)}{4374 (2+3 x)^2} \]

[In]

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

[Out]

(551755 + 2076942*x + 2072124*x^2 + 81702*x^3 + 67230*x^4 + 340200*x^5 - 364500*x^6 - 60438*(2 + 3*x)^2*Log[2
+ 3*x])/(4374*(2 + 3*x)^2)

Maple [A] (verified)

Time = 2.44 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.71

method	result	size
risch	\(-\frac {250 x^{4}}{27}+\frac {1700 x^{3}}{81}-\frac {1795 x^{2}}{81}+\frac {16253 x}{729}+\frac {-\frac {1813 x}{243}-\frac {21413}{4374}}{\left (2+3 x \right )^{2}}-\frac {10073 \ln \left (2+3 x \right )}{729}\)	\(42\)
default	\(\frac {16253 x}{729}-\frac {1795 x^{2}}{81}+\frac {1700 x^{3}}{81}-\frac {250 x^{4}}{27}+\frac {343}{4374 \left (2+3 x \right )^{2}}-\frac {1813}{729 \left (2+3 x \right )}-\frac {10073 \ln \left (2+3 x \right )}{729}\)	\(46\)
norman	\(\frac {\frac {46853}{486} x +\frac {41021}{216} x^{2}+\frac {1513}{81} x^{3}+\frac {415}{27} x^{4}+\frac {700}{9} x^{5}-\frac {250}{3} x^{6}}{\left (2+3 x \right )^{2}}-\frac {10073 \ln \left (2+3 x \right )}{729}\)	\(47\)
parallelrisch	\(-\frac {486000 x^{6}-453600 x^{5}-89640 x^{4}+725256 \ln \left (\frac {2}{3}+x \right ) x^{2}-108936 x^{3}+967008 \ln \left (\frac {2}{3}+x \right ) x -1107567 x^{2}+322336 \ln \left (\frac {2}{3}+x \right )-562236 x}{5832 \left (2+3 x \right )^{2}}\)	\(61\)
meijerg	\(\frac {27 x \left (\frac {3 x}{2}+2\right )}{16 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {27 x^{2}}{16 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {29 x \left (\frac {27 x}{2}+6\right )}{12 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {10073 \ln \left (1+\frac {3 x}{2}\right )}{729}+\frac {179 x \left (9 x^{2}+27 x +12\right )}{108 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {58 x \left (-\frac {135}{8} x^{3}+45 x^{2}+135 x +60\right )}{27 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {200 x \left (\frac {81}{8} x^{4}-\frac {135}{8} x^{3}+45 x^{2}+135 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {2000 x \left (-\frac {1701}{32} x^{5}+\frac {567}{8} x^{4}-\frac {945}{8} x^{3}+315 x^{2}+945 x +420\right )}{5103 \left (1+\frac {3 x}{2}\right )^{2}}\)	\(162\)

[In]

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

[Out]

-250/27*x^4+1700/81*x^3-1795/81*x^2+16253/729*x+9*(-1813/2187*x-21413/39366)/(2+3*x)^2-10073/729*ln(2+3*x)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.05 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx=-\frac {364500 \, x^{6} - 340200 \, x^{5} - 67230 \, x^{4} - 81702 \, x^{3} - 782496 \, x^{2} + 60438 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 357438 \, x + 21413}{4374 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

[In]

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

[Out]

-1/4374*(364500*x^6 - 340200*x^5 - 67230*x^4 - 81702*x^3 - 782496*x^2 + 60438*(9*x^2 + 12*x + 4)*log(3*x + 2)
- 357438*x + 21413)/(9*x^2 + 12*x + 4)

Sympy [A] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.83 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx=- \frac {250 x^{4}}{27} + \frac {1700 x^{3}}{81} - \frac {1795 x^{2}}{81} + \frac {16253 x}{729} - \frac {32634 x + 21413}{39366 x^{2} + 52488 x + 17496} - \frac {10073 \log {\left (3 x + 2 \right )}}{729} \]

[In]

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

[Out]

-250*x**4/27 + 1700*x**3/81 - 1795*x**2/81 + 16253*x/729 - (32634*x + 21413)/(39366*x**2 + 52488*x + 17496) -
10073*log(3*x + 2)/729

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.78 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx=-\frac {250}{27} \, x^{4} + \frac {1700}{81} \, x^{3} - \frac {1795}{81} \, x^{2} + \frac {16253}{729} \, x - \frac {49 \, {\left (666 \, x + 437\right )}}{4374 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {10073}{729} \, \log \left (3 \, x + 2\right ) \]

[In]

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

[Out]

-250/27*x^4 + 1700/81*x^3 - 1795/81*x^2 + 16253/729*x - 49/4374*(666*x + 437)/(9*x^2 + 12*x + 4) - 10073/729*l
og(3*x + 2)

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx=-\frac {250}{27} \, x^{4} + \frac {1700}{81} \, x^{3} - \frac {1795}{81} \, x^{2} + \frac {16253}{729} \, x - \frac {49 \, {\left (666 \, x + 437\right )}}{4374 \, {\left (3 \, x + 2\right )}^{2}} - \frac {10073}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]

[In]

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

[Out]

-250/27*x^4 + 1700/81*x^3 - 1795/81*x^2 + 16253/729*x - 49/4374*(666*x + 437)/(3*x + 2)^2 - 10073/729*log(abs(
3*x + 2))

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx=\frac {16253\,x}{729}-\frac {10073\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {\frac {1813\,x}{2187}+\frac {21413}{39366}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}-\frac {1795\,x^2}{81}+\frac {1700\,x^3}{81}-\frac {250\,x^4}{27} \]

[In]

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

[Out]

(16253*x)/729 - (10073*log(x + 2/3))/729 - ((1813*x)/2187 + 21413/39366)/((4*x)/3 + x^2 + 4/9) - (1795*x^2)/81
+ (1700*x^3)/81 - (250*x^4)/27