3.1473 \(\int \frac{(2+3 x)^2 (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{225 x^5}{2}-\frac{8175 x^4}{16}-\frac{25835 x^3}{24}-\frac{47939 x^2}{32}-\frac{61763 x}{32}-\frac{65219}{64} \log (1-2 x) \]

[Out]

(-61763*x)/32 - (47939*x^2)/32 - (25835*x^3)/24 - (8175*x^4)/16 - (225*x^5)/2 - (65219*Log[1 - 2*x])/64

________________________________________________________________________________________

Rubi [A]  time = 0.0194679, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{225 x^5}{2}-\frac{8175 x^4}{16}-\frac{25835 x^3}{24}-\frac{47939 x^2}{32}-\frac{61763 x}{32}-\frac{65219}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-61763*x)/32 - (47939*x^2)/32 - (25835*x^3)/24 - (8175*x^4)/16 - (225*x^5)/2 - (65219*Log[1 - 2*x])/64

Rule 88

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*} \int \frac{(2+3 x)^2 (3+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac{61763}{32}-\frac{47939 x}{16}-\frac{25835 x^2}{8}-\frac{8175 x^3}{4}-\frac{1125 x^4}{2}-\frac{65219}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac{61763 x}{32}-\frac{47939 x^2}{32}-\frac{25835 x^3}{24}-\frac{8175 x^4}{16}-\frac{225 x^5}{2}-\frac{65219}{64} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0114682, size = 37, normalized size = 0.84 \[ \frac{1}{768} \left (-86400 x^5-392400 x^4-826720 x^3-1150536 x^2-1482312 x-782628 \log (1-2 x)+1159355\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(1159355 - 1482312*x - 1150536*x^2 - 826720*x^3 - 392400*x^4 - 86400*x^5 - 782628*Log[1 - 2*x])/768

________________________________________________________________________________________

Maple [A]  time = 0.003, size = 33, normalized size = 0.8 \begin{align*} -{\frac{225\,{x}^{5}}{2}}-{\frac{8175\,{x}^{4}}{16}}-{\frac{25835\,{x}^{3}}{24}}-{\frac{47939\,{x}^{2}}{32}}-{\frac{61763\,x}{32}}-{\frac{65219\,\ln \left ( 2\,x-1 \right ) }{64}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/2*x^5-8175/16*x^4-25835/24*x^3-47939/32*x^2-61763/32*x-65219/64*ln(2*x-1)

________________________________________________________________________________________

Maxima [A]  time = 1.02213, size = 43, normalized size = 0.98 \begin{align*} -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*log(2*x - 1)

________________________________________________________________________________________

Fricas [A]  time = 1.26818, size = 126, normalized size = 2.86 \begin{align*} -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*log(2*x - 1)

________________________________________________________________________________________

Sympy [A]  time = 0.091516, size = 42, normalized size = 0.95 \begin{align*} - \frac{225 x^{5}}{2} - \frac{8175 x^{4}}{16} - \frac{25835 x^{3}}{24} - \frac{47939 x^{2}}{32} - \frac{61763 x}{32} - \frac{65219 \log{\left (2 x - 1 \right )}}{64} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225*x**5/2 - 8175*x**4/16 - 25835*x**3/24 - 47939*x**2/32 - 61763*x/32 - 65219*log(2*x - 1)/64

________________________________________________________________________________________

Giac [A]  time = 1.35696, size = 45, normalized size = 1.02 \begin{align*} -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*log(abs(2*x - 1))