3.1557 \(\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=62 \[ \frac{2025 x^6}{8}+\frac{6723 x^5}{4}+\frac{342333 x^4}{64}+\frac{89913 x^3}{8}+\frac{2412699 x^2}{128}+\frac{2104901 x}{64}+\frac{2033647}{256 (1-2 x)}+\frac{6206585}{256} \log (1-2 x) \]

[Out]

2033647/(256*(1 - 2*x)) + (2104901*x)/64 + (2412699*x^2)/128 + (89913*x^3)/8 + (342333*x^4)/64 + (6723*x^5)/4
+ (2025*x^6)/8 + (6206585*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0332136, antiderivative size = 62, 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} \[ \frac{2025 x^6}{8}+\frac{6723 x^5}{4}+\frac{342333 x^4}{64}+\frac{89913 x^3}{8}+\frac{2412699 x^2}{128}+\frac{2104901 x}{64}+\frac{2033647}{256 (1-2 x)}+\frac{6206585}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

2033647/(256*(1 - 2*x)) + (2104901*x)/64 + (2412699*x^2)/128 + (89913*x^3)/8 + (342333*x^4)/64 + (6723*x^5)/4
+ (2025*x^6)/8 + (6206585*Log[1 - 2*x])/256

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)^5 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{2104901}{64}+\frac{2412699 x}{64}+\frac{269739 x^2}{8}+\frac{342333 x^3}{16}+\frac{33615 x^4}{4}+\frac{6075 x^5}{4}+\frac{2033647}{128 (-1+2 x)^2}+\frac{6206585}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{2033647}{256 (1-2 x)}+\frac{2104901 x}{64}+\frac{2412699 x^2}{128}+\frac{89913 x^3}{8}+\frac{342333 x^4}{64}+\frac{6723 x^5}{4}+\frac{2025 x^6}{8}+\frac{6206585}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0154388, size = 59, normalized size = 0.95 \[ \frac{518400 x^7+3182976 x^6+9233568 x^5+17540400 x^4+27094320 x^3+48055240 x^2-80685178 x+24826340 (2 x-1) \log (1-2 x)[phone]}{1024 (2 x-1)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(15368793 - 80685178*x + 48055240*x^2 + 27094320*x^3 + 17540400*x^4 + 9233568*x^5 + 3182976*x^6 + 518400*x^7 +
24826340*(-1 + 2*x)*Log[1 - 2*x])/(1024*(-1 + 2*x))

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Maple [A]  time = 0.006, size = 47, normalized size = 0.8 \begin{align*}{\frac{2025\,{x}^{6}}{8}}+{\frac{6723\,{x}^{5}}{4}}+{\frac{342333\,{x}^{4}}{64}}+{\frac{89913\,{x}^{3}}{8}}+{\frac{2412699\,{x}^{2}}{128}}+{\frac{2104901\,x}{64}}+{\frac{6206585\,\ln \left ( 2\,x-1 \right ) }{256}}-{\frac{2033647}{512\,x-256}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2025/8*x^6+6723/4*x^5+342333/64*x^4+89913/8*x^3+2412699/128*x^2+2104901/64*x+6206585/256*ln(2*x-1)-2033647/256
/(2*x-1)

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Maxima [A]  time = 1.06275, size = 62, normalized size = 1. \begin{align*} \frac{2025}{8} \, x^{6} + \frac{6723}{4} \, x^{5} + \frac{342333}{64} \, x^{4} + \frac{89913}{8} \, x^{3} + \frac{2412699}{128} \, x^{2} + \frac{2104901}{64} \, x - \frac{2033647}{256 \,{\left (2 \, x - 1\right )}} + \frac{6206585}{256} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2025/8*x^6 + 6723/4*x^5 + 342333/64*x^4 + 89913/8*x^3 + 2412699/128*x^2 + 2104901/64*x - 2033647/256/(2*x - 1)
+ 6206585/256*log(2*x - 1)

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Fricas [A]  time = 1.32131, size = 209, normalized size = 3.37 \begin{align*} \frac{129600 \, x^{7} + 795744 \, x^{6} + 2308392 \, x^{5} + 4385100 \, x^{4} + 6773580 \, x^{3} + 12013810 \, x^{2} + 6206585 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 8419604 \, x - 2033647}{256 \,{\left (2 \, x - 1\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/256*(129600*x^7 + 795744*x^6 + 2308392*x^5 + 4385100*x^4 + 6773580*x^3 + 12013810*x^2 + 6206585*(2*x - 1)*lo
g(2*x - 1) - 8419604*x - 2033647)/(2*x - 1)

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Sympy [A]  time = 0.10927, size = 54, normalized size = 0.87 \begin{align*} \frac{2025 x^{6}}{8} + \frac{6723 x^{5}}{4} + \frac{342333 x^{4}}{64} + \frac{89913 x^{3}}{8} + \frac{2412699 x^{2}}{128} + \frac{2104901 x}{64} + \frac{6206585 \log{\left (2 x - 1 \right )}}{256} - \frac{2033647}{512 x - 256} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2025*x**6/8 + 6723*x**5/4 + 342333*x**4/64 + 89913*x**3/8 + 2412699*x**2/128 + 2104901*x/64 + 6206585*log(2*x
- 1)/256 - 2033647/(512*x - 256)

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Giac [A]  time = 2.81599, size = 113, normalized size = 1.82 \begin{align*} \frac{1}{1024} \,{\left (2 \, x - 1\right )}^{6}{\left (\frac{78084}{2 \, x - 1} + \frac{672003}{{\left (2 \, x - 1\right )}^{2}} + \frac{3426780}{{\left (2 \, x - 1\right )}^{3}} + \frac{11793810}{{\left (2 \, x - 1\right )}^{4}} + \frac{32468380}{{\left (2 \, x - 1\right )}^{5}} + 4050\right )} - \frac{2033647}{256 \,{\left (2 \, x - 1\right )}} - \frac{6206585}{256} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/1024*(2*x - 1)^6*(78084/(2*x - 1) + 672003/(2*x - 1)^2 + 3426780/(2*x - 1)^3 + 11793810/(2*x - 1)^4 + 324683
80/(2*x - 1)^5 + 4050) - 2033647/256/(2*x - 1) - 6206585/256*log(1/2*abs(2*x - 1)/(2*x - 1)^2)