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

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

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Rubi [A]  time = 0.03, antiderivative size = 62, normalized size of antiderivative = 1.00, 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} \begin {gather*} \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) \end {gather*}

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*}

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Mathematica [A]  time = 0.02, size = 59, normalized size = 0.95 \begin {gather*} \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)} \end {gather*}

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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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^5 (3+5 x)^2}{(1-2 x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.19, size = 57, normalized size = 0.92 \begin {gather*} \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 {gather*}

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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giac [A]  time = 0.80, size = 84, normalized size = 1.35 \begin {gather*} \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 {gather*}

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)

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maple [A]  time = 0.01, size = 47, normalized size = 0.76 \begin {gather*} \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}{256 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x+2)^5*(5*x+3)^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-2033647/256/(2*x-1)+6206585/256*l
n(2*x-1)

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maxima [A]  time = 0.58, size = 46, normalized size = 0.74 \begin {gather*} \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 {gather*}

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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mupad [B]  time = 0.04, size = 44, normalized size = 0.71 \begin {gather*} \frac {2104901\,x}{64}+\frac {6206585\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {2033647}{512\,\left (x-\frac {1}{2}\right )}+\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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(2104901*x)/64 + (6206585*log(x - 1/2))/256 - 2033647/(512*(x - 1/2)) + (2412699*x^2)/128 + (89913*x^3)/8 + (3
42333*x^4)/64 + (6723*x^5)/4 + (2025*x^6)/8

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sympy [A]  time = 0.12, size = 54, normalized size = 0.87 \begin {gather*} \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 {gather*}

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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