3.1439 \(\int \frac {(2+3 x)^3 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac {135 x^4}{8}-\frac {279 x^3}{4}-\frac {2205 x^2}{16}-\frac {3389 x}{16}-\frac {3773}{32} \log (1-2 x) \]

[Out]

-3389/16*x-2205/16*x^2-279/4*x^3-135/8*x^4-3773/32*ln(1-2*x)

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {135 x^4}{8}-\frac {279 x^3}{4}-\frac {2205 x^2}{16}-\frac {3389 x}{16}-\frac {3773}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-3389*x)/16 - (2205*x^2)/16 - (279*x^3)/4 - (135*x^4)/8 - (3773*Log[1 - 2*x])/32

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac {3389}{16}-\frac {2205 x}{8}-\frac {837 x^2}{4}-\frac {135 x^3}{2}-\frac {3773}{16 (-1+2 x)}\right ) \, dx\\ &=-\frac {3389 x}{16}-\frac {2205 x^2}{16}-\frac {279 x^3}{4}-\frac {135 x^4}{8}-\frac {3773}{32} \log (1-2 x)\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.02, size = 32, normalized size = 0.86 \[ \frac {1}{128} \left (-2160 x^4-8928 x^3-17640 x^2-27112 x-15092 \log (1-2 x)+19217\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(19217 - 27112*x - 17640*x^2 - 8928*x^3 - 2160*x^4 - 15092*Log[1 - 2*x])/128

________________________________________________________________________________________

fricas [A]  time = 0.84, size = 27, normalized size = 0.73 \[ -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(2*x - 1)

________________________________________________________________________________________

giac [A]  time = 1.02, size = 28, normalized size = 0.76 \[ -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(abs(2*x - 1))

________________________________________________________________________________________

maple [A]  time = 0.00, size = 28, normalized size = 0.76 \[ -\frac {135 x^{4}}{8}-\frac {279 x^{3}}{4}-\frac {2205 x^{2}}{16}-\frac {3389 x}{16}-\frac {3773 \ln \left (2 x -1\right )}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135/8*x^4-279/4*x^3-2205/16*x^2-3389/16*x-3773/32*ln(2*x-1)

________________________________________________________________________________________

maxima [A]  time = 0.52, size = 27, normalized size = 0.73 \[ -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(2*x - 1)

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 25, normalized size = 0.68 \[ -\frac {3389\,x}{16}-\frac {3773\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {2205\,x^2}{16}-\frac {279\,x^3}{4}-\frac {135\,x^4}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

- (3389*x)/16 - (3773*log(x - 1/2))/32 - (2205*x^2)/16 - (279*x^3)/4 - (135*x^4)/8

________________________________________________________________________________________

sympy [A]  time = 0.10, size = 36, normalized size = 0.97 \[ - \frac {135 x^{4}}{8} - \frac {279 x^{3}}{4} - \frac {2205 x^{2}}{16} - \frac {3389 x}{16} - \frac {3773 \log {\left (2 x - 1 \right )}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135*x**4/8 - 279*x**3/4 - 2205*x**2/16 - 3389*x/16 - 3773*log(2*x - 1)/32

________________________________________________________________________________________