\(\int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx\) [1333]

Optimal result

Integrand size = 22, antiderivative size = 68 \[ \int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {49}{3 (2+3 x)^3}+\frac {707}{2 (2+3 x)^2}+\frac {6934}{2+3 x}-\frac {605}{2 (3+5 x)^2}+\frac {7480}{3+5 x}-57110 \log (2+3 x)+57110 \log (3+5 x) \]

[Out]

49/3/(2+3*x)^3+707/2/(2+3*x)^2+6934/(2+3*x)-605/2/(3+5*x)^2+7480/(3+5*x)-57110*ln(2+3*x)+57110*ln(3+5*x)

Rubi [A] (verified)

Time = 0.03 (sec) , antiderivative size = 68, 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} \[ \int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {6934}{3 x+2}+\frac {7480}{5 x+3}+\frac {707}{2 (3 x+2)^2}-\frac {605}{2 (5 x+3)^2}+\frac {49}{3 (3 x+2)^3}-57110 \log (3 x+2)+57110 \log (5 x+3) \]

[In]

Int[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^3),x]

[Out]

49/(3*(2 + 3*x)^3) + 707/(2*(2 + 3*x)^2) + 6934/(2 + 3*x) - 605/(2*(3 + 5*x)^2) + 7480/(3 + 5*x) - 57110*Log[2
+ 3*x] + 57110*Log[3 + 5*x]

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 {147}{(2+3 x)^4}-\frac {2121}{(2+3 x)^3}-\frac {20802}{(2+3 x)^2}-\frac {171330}{2+3 x}+\frac {3025}{(3+5 x)^3}-\frac {37400}{(3+5 x)^2}+\frac {285550}{3+5 x}\right ) \, dx \\ & = \frac {49}{3 (2+3 x)^3}+\frac {707}{2 (2+3 x)^2}+\frac {6934}{2+3 x}-\frac {605}{2 (3+5 x)^2}+\frac {7480}{3+5 x}-57110 \log (2+3 x)+57110 \log (3+5 x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.03 (sec) , antiderivative size = 70, normalized size of antiderivative = 1.03 \[ \int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {49}{3 (2+3 x)^3}+\frac {707}{2 (2+3 x)^2}+\frac {6934}{2+3 x}-\frac {605}{2 (3+5 x)^2}+\frac {7480}{3+5 x}-57110 \log (5 (2+3 x))+57110 \log (3+5 x) \]

[In]

Integrate[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^3),x]

[Out]

49/(3*(2 + 3*x)^3) + 707/(2*(2 + 3*x)^2) + 6934/(2 + 3*x) - 605/(2*(3 + 5*x)^2) + 7480/(3 + 5*x) - 57110*Log[5
*(2 + 3*x)] + 57110*Log[3 + 5*x]

Maple [A] (verified)

Time = 2.36 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.78

method	result	size
norman	\(\frac {2569950 x^{4}+6596205 x^{3}+\frac {5416693}{2} x +\frac {19029052}{3} x^{2}+433234}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-57110 \ln \left (2+3 x \right )+57110 \ln \left (3+5 x \right )\)	\(53\)
risch	\(\frac {2569950 x^{4}+6596205 x^{3}+\frac {5416693}{2} x +\frac {19029052}{3} x^{2}+433234}{\left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-57110 \ln \left (2+3 x \right )+57110 \ln \left (3+5 x \right )\)	\(54\)
default	\(\frac {49}{3 \left (2+3 x \right )^{3}}+\frac {707}{2 \left (2+3 x \right )^{2}}+\frac {6934}{2+3 x}-\frac {605}{2 \left (3+5 x \right )^{2}}+\frac {7480}{3+5 x}-57110 \ln \left (2+3 x \right )+57110 \ln \left (3+5 x \right )\)	\(63\)
parallelrisch	\(-\frac {2775546000 \ln \left (\frac {2}{3}+x \right ) x^{5}-2775546000 \ln \left (x +\frac {3}{5}\right ) x^{5}[phone] \ln \left (\frac {2}{3}+x \right ) x^{4}-8881747200 \ln \left (x +\frac {3}{5}\right ) x^{4}[phone] x^{5}[phone] \ln \left (\frac {2}{3}+x \right ) x^{3}-11361234960 \ln \left (x +\frac {3}{5}\right ) x^{3}[phone] x^{4}[phone] \ln \left (\frac {2}{3}+x \right ) x^{2}-7261650720 \ln \left (x +\frac {3}{5}\right ) x^{2}[phone] x^{3}[phone] \ln \left (\frac {2}{3}+x \right ) x -2319122880 \ln \left (x +\frac {3}{5}\right ) x [phone] x^{2}[phone] \ln \left (\frac {2}{3}+x \right )-296058240 \ln \left (x +\frac {3}{5}\right )[phone] x}{72 \left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}\)	\(139\)

[In]

int((1-2*x)^2/(2+3*x)^4/(3+5*x)^3,x,method=_RETURNVERBOSE)

[Out]

(2569950*x^4+6596205*x^3+5416693/2*x+19029052/3*x^2+433234)/(2+3*x)^3/(3+5*x)^2-57110*ln(2+3*x)+57110*ln(3+5*x
)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 115, normalized size of antiderivative = 1.69 \[ \int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 342660 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 342660 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) + 16250079 \, x + 2599404}{6 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \]

[In]

integrate((1-2*x)^2/(2+3*x)^4/(3+5*x)^3,x, algorithm="fricas")

[Out]

1/6*(15419700*x^4 + 39577230*x^3 + 38058104*x^2 + 342660*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 7
2)*log(5*x + 3) - 342660*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(3*x + 2) + 16250079*x + 2
599404)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)

Sympy [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.90 \[ \int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {15419700 x^{4} + 39577230 x^{3} + 38058104 x^{2} + 16250079 x + 2599404}{4050 x^{5} + 12960 x^{4} + 16578 x^{3} + 10596 x^{2} + 3384 x + 432} + 57110 \log {\left (x + \frac {3}{5} \right )} - 57110 \log {\left (x + \frac {2}{3} \right )} \]

[In]

integrate((1-2*x)**2/(2+3*x)**4/(3+5*x)**3,x)

[Out]

(15419700*x**4 + 39577230*x**3 + 38058104*x**2 + 16250079*x + 2599404)/(4050*x**5 + 12960*x**4 + 16578*x**3 +
10596*x**2 + 3384*x + 432) + 57110*log(x + 3/5) - 57110*log(x + 2/3)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.97 \[ \int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 16250079 \, x + 2599404}{6 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + 57110 \, \log \left (5 \, x + 3\right ) - 57110 \, \log \left (3 \, x + 2\right ) \]

[In]

integrate((1-2*x)^2/(2+3*x)^4/(3+5*x)^3,x, algorithm="maxima")

[Out]

1/6*(15419700*x^4 + 39577230*x^3 + 38058104*x^2 + 16250079*x + 2599404)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*
x^2 + 564*x + 72) + 57110*log(5*x + 3) - 57110*log(3*x + 2)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.81 \[ \int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 16250079 \, x + 2599404}{6 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{3}} + 57110 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 57110 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]

[In]

integrate((1-2*x)^2/(2+3*x)^4/(3+5*x)^3,x, algorithm="giac")

[Out]

1/6*(15419700*x^4 + 39577230*x^3 + 38058104*x^2 + 16250079*x + 2599404)/((5*x + 3)^2*(3*x + 2)^3) + 57110*log(
abs(5*x + 3)) - 57110*log(abs(3*x + 2))

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.81 \[ \int \frac {(1-2 x)^2}{(2+3 x)^4 (3+5 x)^3} \, dx=\frac {\frac {11422\,x^4}{3}+\frac {439747\,x^3}{45}+\frac {19029052\,x^2}{2025}+\frac {5416693\,x}{1350}+\frac {433234}{675}}{x^5+\frac {16\,x^4}{5}+\frac {307\,x^3}{75}+\frac {1766\,x^2}{675}+\frac {188\,x}{225}+\frac {8}{75}}-114220\,\mathrm {atanh}\left (30\,x+19\right ) \]

[In]

int((2*x - 1)^2/((3*x + 2)^4*(5*x + 3)^3),x)

[Out]

((5416693*x)/1350 + (19029052*x^2)/2025 + (439747*x^3)/45 + (11422*x^4)/3 + 433234/675)/((188*x)/225 + (1766*x
^2)/675 + (307*x^3)/75 + (16*x^4)/5 + x^5 + 8/75) - 114220*atanh(30*x + 19)