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

Optimal. Leaf size=44 \[ -\frac {225 x^5}{2}-\frac {8175 x^4}{16}-\frac {25835 x^3}{24}-\frac {47939 x^2}{32}-\frac {61763 x}{32}-\frac {65219}{64} \log (1-2 x) \]

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Rubi [A]  time = 0.02, antiderivative size = 44, 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^5}{2}-\frac {8175 x^4}{16}-\frac {25835 x^3}{24}-\frac {47939 x^2}{32}-\frac {61763 x}{32}-\frac {65219}{64} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-61763*x)/32 - (47939*x^2)/32 - (25835*x^3)/24 - (8175*x^4)/16 - (225*x^5)/2 - (65219*Log[1 - 2*x])/64

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)^3}{1-2 x} \, dx &=\int \left (-\frac {61763}{32}-\frac {47939 x}{16}-\frac {25835 x^2}{8}-\frac {8175 x^3}{4}-\frac {1125 x^4}{2}-\frac {65219}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac {61763 x}{32}-\frac {47939 x^2}{32}-\frac {25835 x^3}{24}-\frac {8175 x^4}{16}-\frac {225 x^5}{2}-\frac {65219}{64} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.01, size = 37, normalized size = 0.84 \begin {gather*} \frac {1}{768} \left (-86400 x^5-392400 x^4-826720 x^3-1150536 x^2-1482312 x-782628 \log (1-2 x)+1159355\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(1159355 - 1482312*x - 1150536*x^2 - 826720*x^3 - 392400*x^4 - 86400*x^5 - 782628*Log[1 - 2*x])/768

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

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.04, size = 32, normalized size = 0.73 \begin {gather*} -\frac {225}{2} \, x^{5} - \frac {8175}{16} \, x^{4} - \frac {25835}{24} \, x^{3} - \frac {47939}{32} \, x^{2} - \frac {61763}{32} \, x - \frac {65219}{64} \, \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),x, algorithm="fricas")

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*log(2*x - 1)

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giac [A]  time = 0.91, size = 33, normalized size = 0.75 \begin {gather*} -\frac {225}{2} \, x^{5} - \frac {8175}{16} \, x^{4} - \frac {25835}{24} \, x^{3} - \frac {47939}{32} \, x^{2} - \frac {61763}{32} \, x - \frac {65219}{64} \, \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),x, algorithm="giac")

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*log(abs(2*x - 1))

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maple [A]  time = 0.00, size = 33, normalized size = 0.75 \begin {gather*} -\frac {225 x^{5}}{2}-\frac {8175 x^{4}}{16}-\frac {25835 x^{3}}{24}-\frac {47939 x^{2}}{32}-\frac {61763 x}{32}-\frac {65219 \ln \left (2 x -1\right )}{64} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225/2*x^5-8175/16*x^4-25835/24*x^3-47939/32*x^2-61763/32*x-65219/64*ln(2*x-1)

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maxima [A]  time = 0.49, size = 32, normalized size = 0.73 \begin {gather*} -\frac {225}{2} \, x^{5} - \frac {8175}{16} \, x^{4} - \frac {25835}{24} \, x^{3} - \frac {47939}{32} \, x^{2} - \frac {61763}{32} \, x - \frac {65219}{64} \, \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),x, algorithm="maxima")

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*log(2*x - 1)

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mupad [B]  time = 0.03, size = 30, normalized size = 0.68 \begin {gather*} -\frac {61763\,x}{32}-\frac {65219\,\ln \left (x-\frac {1}{2}\right )}{64}-\frac {47939\,x^2}{32}-\frac {25835\,x^3}{24}-\frac {8175\,x^4}{16}-\frac {225\,x^5}{2} \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),x)

[Out]

- (61763*x)/32 - (65219*log(x - 1/2))/64 - (47939*x^2)/32 - (25835*x^3)/24 - (8175*x^4)/16 - (225*x^5)/2

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sympy [A]  time = 0.11, size = 42, normalized size = 0.95 \begin {gather*} - \frac {225 x^{5}}{2} - \frac {8175 x^{4}}{16} - \frac {25835 x^{3}}{24} - \frac {47939 x^{2}}{32} - \frac {61763 x}{32} - \frac {65219 \log {\left (2 x - 1 \right )}}{64} \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),x)

[Out]

-225*x**5/2 - 8175*x**4/16 - 25835*x**3/24 - 47939*x**2/32 - 61763*x/32 - 65219*log(2*x - 1)/64

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