3.16.59 \(\int \frac {(2+3 x)^3 (3+5 x)^2}{(1-2 x)^2} \, dx\) [1559]

Optimal. Leaf size=48 \[ \frac {41503}{64 (1-2 x)}+\frac {12973 x}{8}+\frac {21717 x^2}{32}+\frac {945 x^3}{4}+\frac {675 x^4}{16}+\frac {91091}{64} \log (1-2 x) \]

[Out]

41503/64/(1-2*x)+12973/8*x+21717/32*x^2+945/4*x^3+675/16*x^4+91091/64*ln(1-2*x)

________________________________________________________________________________________

Rubi [A]
time = 0.02, antiderivative size = 48, 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 {675 x^4}{16}+\frac {945 x^3}{4}+\frac {21717 x^2}{32}+\frac {12973 x}{8}+\frac {41503}{64 (1-2 x)}+\frac {91091}{64} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

41503/(64*(1 - 2*x)) + (12973*x)/8 + (21717*x^2)/32 + (945*x^3)/4 + (675*x^4)/16 + (91091*Log[1 - 2*x])/64

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)^3 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac {12973}{8}+\frac {21717 x}{16}+\frac {2835 x^2}{4}+\frac {675 x^3}{4}+\frac {41503}{32 (-1+2 x)^2}+\frac {91091}{32 (-1+2 x)}\right ) \, dx\\ &=\frac {41503}{64 (1-2 x)}+\frac {12973 x}{8}+\frac {21717 x^2}{32}+\frac {945 x^3}{4}+\frac {675 x^4}{16}+\frac {91091}{64} \log (1-2 x)\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 0.01, size = 49, normalized size = 1.02 \begin {gather*} \frac {93225-933610 x+656536 x^2+286992 x^3+110160 x^4+21600 x^5+364364 (-1+2 x) \log (1-2 x)}{256 (-1+2 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(93225 - 933610*x + 656536*x^2 + 286992*x^3 + 110160*x^4 + 21600*x^5 + 364364*(-1 + 2*x)*Log[1 - 2*x])/(256*(-
1 + 2*x))

________________________________________________________________________________________

Maple [A]
time = 0.10, size = 37, normalized size = 0.77

method	result	size
risch	\(\frac {675 x^{4}}{16}+\frac {945 x^{3}}{4}+\frac {21717 x^{2}}{32}+\frac {12973 x}{8}-\frac {41503}{128 \left (-\frac {1}{2}+x \right )}+\frac {91091 \ln \left (-1+2 x \right )}{64}\)	\(35\)
default	\(\frac {675 x^{4}}{16}+\frac {945 x^{3}}{4}+\frac {21717 x^{2}}{32}+\frac {12973 x}{8}-\frac {41503}{64 \left (-1+2 x \right )}+\frac {91091 \ln \left (-1+2 x \right )}{64}\)	\(37\)
norman	\(\frac {-\frac {93395}{32} x +\frac {82067}{32} x^{2}+\frac {17937}{16} x^{3}+\frac {6885}{16} x^{4}+\frac {675}{8} x^{5}}{-1+2 x}+\frac {91091 \ln \left (-1+2 x \right )}{64}\)	\(42\)
meijerg	\(\frac {354 x}{1-2 x}+\frac {91091 \ln \left (1-2 x \right )}{64}+\frac {883 x \left (-6 x +6\right )}{6 \left (1-2 x \right )}+\frac {2763 x \left (-8 x^{2}-12 x +12\right )}{32 \left (1-2 x \right )}+\frac {9 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{1-2 x}+\frac {225 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{128 \left (1-2 x \right )}\)	\(110\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

675/16*x^4+945/4*x^3+21717/32*x^2+12973/8*x-41503/64/(-1+2*x)+91091/64*ln(-1+2*x)

________________________________________________________________________________________

Maxima [A]
time = 0.29, size = 36, normalized size = 0.75 \begin {gather*} \frac {675}{16} \, x^{4} + \frac {945}{4} \, x^{3} + \frac {21717}{32} \, x^{2} + \frac {12973}{8} \, x - \frac {41503}{64 \, {\left (2 \, x - 1\right )}} + \frac {91091}{64} \, \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)^2,x, algorithm="maxima")

[Out]

675/16*x^4 + 945/4*x^3 + 21717/32*x^2 + 12973/8*x - 41503/64/(2*x - 1) + 91091/64*log(2*x - 1)

________________________________________________________________________________________

Fricas [A]
time = 0.63, size = 47, normalized size = 0.98 \begin {gather*} \frac {5400 \, x^{5} + 27540 \, x^{4} + 71748 \, x^{3} + 164134 \, x^{2} + 91091 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 103784 \, x - 41503}{64 \, {\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)^2,x, algorithm="fricas")

[Out]

1/64*(5400*x^5 + 27540*x^4 + 71748*x^3 + 164134*x^2 + 91091*(2*x - 1)*log(2*x - 1) - 103784*x - 41503)/(2*x -
1)

________________________________________________________________________________________

Sympy [A]
time = 0.04, size = 41, normalized size = 0.85 \begin {gather*} \frac {675 x^{4}}{16} + \frac {945 x^{3}}{4} + \frac {21717 x^{2}}{32} + \frac {12973 x}{8} + \frac {91091 \log {\left (2 x - 1 \right )}}{64} - \frac {41503}{128 x - 64} \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)**2,x)

[Out]

675*x**4/16 + 945*x**3/4 + 21717*x**2/32 + 12973*x/8 + 91091*log(2*x - 1)/64 - 41503/(128*x - 64)

________________________________________________________________________________________

Giac [A]
time = 0.95, size = 66, normalized size = 1.38 \begin {gather*} \frac {1}{256} \, {\left (2 \, x - 1\right )}^{4} {\left (\frac {10260}{2 \, x - 1} + \frac {70164}{{\left (2 \, x - 1\right )}^{2}} + \frac {319816}{{\left (2 \, x - 1\right )}^{3}} + 675\right )} - \frac {41503}{64 \, {\left (2 \, x - 1\right )}} - \frac {91091}{64} \, \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)^3*(3+5*x)^2/(1-2*x)^2,x, algorithm="giac")

[Out]

1/256*(2*x - 1)^4*(10260/(2*x - 1) + 70164/(2*x - 1)^2 + 319816/(2*x - 1)^3 + 675) - 41503/64/(2*x - 1) - 9109
1/64*log(1/2*abs(2*x - 1)/(2*x - 1)^2)

________________________________________________________________________________________

Mupad [B]
time = 0.03, size = 34, normalized size = 0.71 \begin {gather*} \frac {12973\,x}{8}+\frac {91091\,\ln \left (x-\frac {1}{2}\right )}{64}-\frac {41503}{128\,\left (x-\frac {1}{2}\right )}+\frac {21717\,x^2}{32}+\frac {945\,x^3}{4}+\frac {675\,x^4}{16} \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)^2,x)

[Out]

(12973*x)/8 + (91091*log(x - 1/2))/64 - 41503/(128*(x - 1/2)) + (21717*x^2)/32 + (945*x^3)/4 + (675*x^4)/16

________________________________________________________________________________________