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

Optimal. Leaf size=52 \[ -\frac {225 x^3}{8}-\frac {6345 x^2}{32}-\frac {14031 x}{16}-\frac {91091}{64 (1-2 x)}+\frac {41503}{128 (1-2 x)^2}-\frac {39977}{32} \log (1-2 x) \]

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Rubi [A]  time = 0.02, antiderivative size = 52, 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 {225 x^3}{8}-\frac {6345 x^2}{32}-\frac {14031 x}{16}-\frac {91091}{64 (1-2 x)}+\frac {41503}{128 (1-2 x)^2}-\frac {39977}{32} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

41503/(128*(1 - 2*x)^2) - 91091/(64*(1 - 2*x)) - (14031*x)/16 - (6345*x^2)/32 - (225*x^3)/8 - (39977*Log[1 - 2
*x])/32

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)^3 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {14031}{16}-\frac {6345 x}{16}-\frac {675 x^2}{8}-\frac {41503}{32 (-1+2 x)^3}-\frac {91091}{32 (-1+2 x)^2}-\frac {39977}{16 (-1+2 x)}\right ) \, dx\\ &=\frac {41503}{128 (1-2 x)^2}-\frac {91091}{64 (1-2 x)}-\frac {14031 x}{16}-\frac {6345 x^2}{32}-\frac {225 x^3}{8}-\frac {39977}{32} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 47, normalized size = 0.90 \begin {gather*} \frac {1}{32} \left (-\frac {2 \left (1800 x^5+10890 x^4+43884 x^3-84411 x^2-55 x+9720\right )}{(1-2 x)^2}-39977 \log (1-2 x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((-2*(9720 - 55*x - 84411*x^2 + 43884*x^3 + 10890*x^4 + 1800*x^5))/(1 - 2*x)^2 - 39977*Log[1 - 2*x])/32

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

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.69, size = 57, normalized size = 1.10 \begin {gather*} -\frac {14400 \, x^{5} + 87120 \, x^{4} + 351072 \, x^{3} - 423612 \, x^{2} + 159908 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 252116 \, x + 140679}{128 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/128*(14400*x^5 + 87120*x^4 + 351072*x^3 - 423612*x^2 + 159908*(4*x^2 - 4*x + 1)*log(2*x - 1) - 252116*x + 1
40679)/(4*x^2 - 4*x + 1)

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giac [A]  time = 1.17, size = 37, normalized size = 0.71 \begin {gather*} -\frac {225}{8} \, x^{3} - \frac {6345}{32} \, x^{2} - \frac {14031}{16} \, x + \frac {539 \, {\left (676 \, x - 261\right )}}{128 \, {\left (2 \, x - 1\right )}^{2}} - \frac {39977}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/8*x^3 - 6345/32*x^2 - 14031/16*x + 539/128*(676*x - 261)/(2*x - 1)^2 - 39977/32*log(abs(2*x - 1))

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maple [A]  time = 0.01, size = 41, normalized size = 0.79 \begin {gather*} -\frac {225 x^{3}}{8}-\frac {6345 x^{2}}{32}-\frac {14031 x}{16}-\frac {39977 \ln \left (2 x -1\right )}{32}+\frac {41503}{128 \left (2 x -1\right )^{2}}+\frac {91091}{64 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/8*x^3-6345/32*x^2-14031/16*x+41503/128/(2*x-1)^2+91091/64/(2*x-1)-39977/32*ln(2*x-1)

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maxima [A]  time = 0.52, size = 41, normalized size = 0.79 \begin {gather*} -\frac {225}{8} \, x^{3} - \frac {6345}{32} \, x^{2} - \frac {14031}{16} \, x + \frac {539 \, {\left (676 \, x - 261\right )}}{128 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {39977}{32} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/8*x^3 - 6345/32*x^2 - 14031/16*x + 539/128*(676*x - 261)/(4*x^2 - 4*x + 1) - 39977/32*log(2*x - 1)

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mupad [B]  time = 0.03, size = 36, normalized size = 0.69 \begin {gather*} \frac {\frac {91091\,x}{128}-\frac {140679}{512}}{x^2-x+\frac {1}{4}}-\frac {39977\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {14031\,x}{16}-\frac {6345\,x^2}{32}-\frac {225\,x^3}{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((91091*x)/128 - 140679/512)/(x^2 - x + 1/4) - (39977*log(x - 1/2))/32 - (14031*x)/16 - (6345*x^2)/32 - (225*x
^3)/8

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sympy [A]  time = 0.14, size = 44, normalized size = 0.85 \begin {gather*} - \frac {225 x^{3}}{8} - \frac {6345 x^{2}}{32} - \frac {14031 x}{16} - \frac {140679 - 364364 x}{512 x^{2} - 512 x + 128} - \frac {39977 \log {\left (2 x - 1 \right )}}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225*x**3/8 - 6345*x**2/32 - 14031*x/16 - (140679 - 364364*x)/(512*x**2 - 512*x + 128) - 39977*log(2*x - 1)/32

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