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)-1815/16*x-225/16*x^2-3467/16*ln(1-2*x)

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Rubi [A]  time = 0.02, antiderivative size = 45, 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} \[ -\frac {225 x^2}{16}-\frac {1815 x}{16}-\frac {1309}{4 (1-2 x)}+\frac {5929}{64 (1-2 x)^2}-\frac {3467}{16} \log (1-2 x) \]

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*}

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Mathematica [A]  time = 0.02, 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]

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

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fricas [A]  time = 0.84, size = 52, normalized size = 1.16 \[ -\frac {3600 \, x^{4} + 25440 \, x^{3} - 28140 \, x^{2} + 13868 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 34628 \, x + 15015}{64 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

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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giac [A]  time = 1.15, size = 32, normalized size = 0.71 \[ -\frac {225}{16} \, x^{2} - \frac {1815}{16} \, x + \frac {77 \, {\left (544 \, x - 195\right )}}{64 \, {\left (2 \, x - 1\right )}^{2}} - \frac {3467}{16} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

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))

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maple [A]  time = 0.01, size = 36, normalized size = 0.80 \[ -\frac {225 x^{2}}{16}-\frac {1815 x}{16}-\frac {3467 \ln \left (2 x -1\right )}{16}+\frac {5929}{64 \left (2 x -1\right )^{2}}+\frac {1309}{4 \left (2 x -1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.49, size = 36, normalized size = 0.80 \[ -\frac {225}{16} \, x^{2} - \frac {1815}{16} \, x + \frac {77 \, {\left (544 \, x - 195\right )}}{64 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {3467}{16} \, \log \left (2 \, x - 1\right ) \]

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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mupad [B]  time = 0.03, size = 31, normalized size = 0.69 \[ \frac {\frac {1309\,x}{8}-\frac {15015}{256}}{x^2-x+\frac {1}{4}}-\frac {3467\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {1815\,x}{16}-\frac {225\,x^2}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((1309*x)/8 - 15015/256)/(x^2 - x + 1/4) - (3467*log(x - 1/2))/16 - (1815*x)/16 - (225*x^2)/16

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sympy [A]  time = 0.14, size = 37, normalized size = 0.82 \[ - \frac {225 x^{2}}{16} - \frac {1815 x}{16} - \frac {15015 - 41888 x}{256 x^{2} - 256 x + 64} - \frac {3467 \log {\left (2 x - 1 \right )}}{16} \]

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

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