3.1650 \(\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{225 x^2}{16}-\frac{1815 x}{16}-\frac{1309}{4 (1-2 x)}+\frac{5929}{64 (1-2 x)^2}-\frac{3467}{16} \log (1-2 x) \]

[Out]

5929/(64*(1 - 2*x)^2) - 1309/(4*(1 - 2*x)) - (1815*x)/16 - (225*x^2)/16 - (3467*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0212203, antiderivative size = 45, 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} \[ -\frac{225 x^2}{16}-\frac{1815 x}{16}-\frac{1309}{4 (1-2 x)}+\frac{5929}{64 (1-2 x)^2}-\frac{3467}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

5929/(64*(1 - 2*x)^2) - 1309/(4*(1 - 2*x)) - (1815*x)/16 - (225*x^2)/16 - (3467*Log[1 - 2*x])/16

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)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac{1815}{16}-\frac{225 x}{8}-\frac{5929}{16 (-1+2 x)^3}-\frac{1309}{2 (-1+2 x)^2}-\frac{3467}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{5929}{64 (1-2 x)^2}-\frac{1309}{4 (1-2 x)}-\frac{1815 x}{16}-\frac{225 x^2}{16}-\frac{3467}{16} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0145587, size = 46, normalized size = 1.02 \[ -\frac{900 x^4+6360 x^3-10890 x^2-4802 x+3467 (1-2 x)^2 \log (1-2 x)+2790}{16 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-(2790 - 4802*x - 10890*x^2 + 6360*x^3 + 900*x^4 + 3467*(1 - 2*x)^2*Log[1 - 2*x])/(16*(1 - 2*x)^2)

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Maple [A]  time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{225\,{x}^{2}}{16}}-{\frac{1815\,x}{16}}-{\frac{3467\,\ln \left ( 2\,x-1 \right ) }{16}}+{\frac{5929}{64\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{1309}{8\,x-4}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/16*x^2-1815/16*x-3467/16*ln(2*x-1)+5929/64/(2*x-1)^2+1309/4/(2*x-1)

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Maxima [A]  time = 1.14777, size = 49, normalized size = 1.09 \begin{align*} -\frac{225}{16} \, x^{2} - \frac{1815}{16} \, x + \frac{77 \,{\left (544 \, x - 195\right )}}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{3467}{16} \, \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)^2/(1-2*x)^3,x, algorithm="maxima")

[Out]

-225/16*x^2 - 1815/16*x + 77/64*(544*x - 195)/(4*x^2 - 4*x + 1) - 3467/16*log(2*x - 1)

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Fricas [A]  time = 1.47129, size = 158, normalized size = 3.51 \begin{align*} -\frac{3600 \, x^{4} + 25440 \, x^{3} - 28140 \, x^{2} + 13868 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 34628 \, x + 15015}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/64*(3600*x^4 + 25440*x^3 - 28140*x^2 + 13868*(4*x^2 - 4*x + 1)*log(2*x - 1) - 34628*x + 15015)/(4*x^2 - 4*x
+ 1)

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Sympy [A]  time = 0.118582, size = 36, normalized size = 0.8 \begin{align*} - \frac{225 x^{2}}{16} - \frac{1815 x}{16} + \frac{41888 x - 15015}{256 x^{2} - 256 x + 64} - \frac{3467 \log{\left (2 x - 1 \right )}}{16} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225*x**2/16 - 1815*x/16 + (41888*x - 15015)/(256*x**2 - 256*x + 64) - 3467*log(2*x - 1)/16

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Giac [A]  time = 2.68034, size = 43, normalized size = 0.96 \begin{align*} -\frac{225}{16} \, x^{2} - \frac{1815}{16} \, x + \frac{77 \,{\left (544 \, x - 195\right )}}{64 \,{\left (2 \, x - 1\right )}^{2}} - \frac{3467}{16} \, \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)^2/(1-2*x)^3,x, algorithm="giac")

[Out]

-225/16*x^2 - 1815/16*x + 77/64*(544*x - 195)/(2*x - 1)^2 - 3467/16*log(abs(2*x - 1))