3.17.63 \(\int \frac {(2+3 x)^2 (3+5 x)^3}{(1-2 x)^3} \, dx\) [1663]

Optimal. Leaf size=52 \[ \frac {65219}{128 (1-2 x)^2}-\frac {144837}{64 (1-2 x)}-\frac {5695 x}{4}-\frac {10425 x^2}{32}-\frac {375 x^3}{8}-\frac {64317}{32} \log (1-2 x) \]

[Out]

65219/128/(1-2*x)^2-144837/64/(1-2*x)-5695/4*x-10425/32*x^2-375/8*x^3-64317/32*ln(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 = {90} \begin {gather*} -\frac {375 x^3}{8}-\frac {10425 x^2}{32}-\frac {5695 x}{4}-\frac {144837}{64 (1-2 x)}+\frac {65219}{128 (1-2 x)^2}-\frac {64317}{32} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

65219/(128*(1 - 2*x)^2) - 144837/(64*(1 - 2*x)) - (5695*x)/4 - (10425*x^2)/32 - (375*x^3)/8 - (64317*Log[1 - 2
*x])/32

Rule 90

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)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {5695}{4}-\frac {10425 x}{16}-\frac {1125 x^2}{8}-\frac {65219}{32 (-1+2 x)^3}-\frac {144837}{32 (-1+2 x)^2}-\frac {64317}{16 (-1+2 x)}\right ) \, dx\\ &=\frac {65219}{128 (1-2 x)^2}-\frac {144837}{64 (1-2 x)}-\frac {5695 x}{4}-\frac {10425 x^2}{32}-\frac {375 x^3}{8}-\frac {64317}{32} \log (1-2 x)\\ \end {align*}

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Mathematica [A]
time = 0.02, size = 47, normalized size = 0.90 \begin {gather*} \frac {1}{32} \left (-\frac {2 \left (15270+1509 x-137055 x^2+71020 x^3+17850 x^4+3000 x^5\right )}{(1-2 x)^2}-64317 \log (1-2 x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((-2*(15270 + 1509*x - 137055*x^2 + 71020*x^3 + 17850*x^4 + 3000*x^5))/(1 - 2*x)^2 - 64317*Log[1 - 2*x])/32

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Maple [A]
time = 0.10, size = 41, normalized size = 0.79

method	result	size
risch	\(-\frac {375 x^{3}}{8}-\frac {10425 x^{2}}{32}-\frac {5695 x}{4}+\frac {\frac {144837 x}{32}-\frac {224455}{128}}{\left (-1+2 x \right )^{2}}-\frac {64317 \ln \left (-1+2 x \right )}{32}\)	\(37\)
default	\(-\frac {375 x^{3}}{8}-\frac {10425 x^{2}}{32}-\frac {5695 x}{4}+\frac {144837}{64 \left (-1+2 x \right )}+\frac {65219}{128 \left (-1+2 x \right )^{2}}-\frac {64317 \ln \left (-1+2 x \right )}{32}\)	\(41\)
norman	\(\frac {-\frac {62589}{16} x +\frac {198135}{16} x^{2}-\frac {17755}{4} x^{3}-\frac {8925}{8} x^{4}-\frac {375}{2} x^{5}}{\left (-1+2 x \right )^{2}}-\frac {64317 \ln \left (-1+2 x \right )}{32}\)	\(42\)
meijerg	\(\frac {54 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {432 x^{2}}{\left (1-2 x \right )^{2}}-\frac {921 x \left (-18 x +6\right )}{8 \left (1-2 x \right )^{2}}-\frac {64317 \ln \left (1-2 x \right )}{32}-\frac {4415 x \left (16 x^{2}-36 x +12\right )}{32 \left (1-2 x \right )^{2}}-\frac {705 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{32 \left (1-2 x \right )^{2}}-\frac {375 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{64 \left (1-2 x \right )^{2}}\)	\(127\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-375/8*x^3-10425/32*x^2-5695/4*x+144837/64/(-1+2*x)+65219/128/(-1+2*x)^2-64317/32*ln(-1+2*x)

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Maxima [A]
time = 0.31, size = 41, normalized size = 0.79 \begin {gather*} -\frac {375}{8} \, x^{3} - \frac {10425}{32} \, x^{2} - \frac {5695}{4} \, x + \frac {847 \, {\left (684 \, x - 265\right )}}{128 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {64317}{32} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-375/8*x^3 - 10425/32*x^2 - 5695/4*x + 847/128*(684*x - 265)/(4*x^2 - 4*x + 1) - 64317/32*log(2*x - 1)

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Fricas [A]
time = 0.43, size = 57, normalized size = 1.10 \begin {gather*} -\frac {24000 \, x^{5} + 142800 \, x^{4} + 568160 \, x^{3} - 687260 \, x^{2} + 257268 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 397108 \, x + 224455}{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)^2*(3+5*x)^3/(1-2*x)^3,x, algorithm="fricas")

[Out]

-1/128*(24000*x^5 + 142800*x^4 + 568160*x^3 - 687260*x^2 + 257268*(4*x^2 - 4*x + 1)*log(2*x - 1) - 397108*x +
224455)/(4*x^2 - 4*x + 1)

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Sympy [A]
time = 0.05, size = 44, normalized size = 0.85 \begin {gather*} - \frac {375 x^{3}}{8} - \frac {10425 x^{2}}{32} - \frac {5695 x}{4} - \frac {224455 - 579348 x}{512 x^{2} - 512 x + 128} - \frac {64317 \log {\left (2 x - 1 \right )}}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-375*x**3/8 - 10425*x**2/32 - 5695*x/4 - (224455 - 579348*x)/(512*x**2 - 512*x + 128) - 64317*log(2*x - 1)/32

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Giac [A]
time = 1.43, size = 37, normalized size = 0.71 \begin {gather*} -\frac {375}{8} \, x^{3} - \frac {10425}{32} \, x^{2} - \frac {5695}{4} \, x + \frac {847 \, {\left (684 \, x - 265\right )}}{128 \, {\left (2 \, x - 1\right )}^{2}} - \frac {64317}{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)^2*(3+5*x)^3/(1-2*x)^3,x, algorithm="giac")

[Out]

-375/8*x^3 - 10425/32*x^2 - 5695/4*x + 847/128*(684*x - 265)/(2*x - 1)^2 - 64317/32*log(abs(2*x - 1))

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Mupad [B]
time = 0.03, size = 36, normalized size = 0.69 \begin {gather*} \frac {\frac {144837\,x}{128}-\frac {224455}{512}}{x^2-x+\frac {1}{4}}-\frac {64317\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {5695\,x}{4}-\frac {10425\,x^2}{32}-\frac {375\,x^3}{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((144837*x)/128 - 224455/512)/(x^2 - x + 1/4) - (64317*log(x - 1/2))/32 - (5695*x)/4 - (10425*x^2)/32 - (375*x
^3)/8

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