3.1459 \(\int \frac{(3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=23 \[ -\frac{25 x^2}{4}-\frac{85 x}{4}-\frac{121}{8} \log (1-2 x) \]

[Out]

(-85*x)/4 - (25*x^2)/4 - (121*Log[1 - 2*x])/8

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Rubi [A]  time = 0.0088048, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{25 x^2}{4}-\frac{85 x}{4}-\frac{121}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

Int[(3 + 5*x)^2/(1 - 2*x),x]

[Out]

(-85*x)/4 - (25*x^2)/4 - (121*Log[1 - 2*x])/8

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

\begin{align*} \int \frac{(3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac{85}{4}-\frac{25 x}{2}-\frac{121}{4 (-1+2 x)}\right ) \, dx\\ &=-\frac{85 x}{4}-\frac{25 x^2}{4}-\frac{121}{8} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0059653, size = 25, normalized size = 1.09 \[ \frac{1}{16} \left (-5 \left (20 x^2+68 x-39\right )-242 \log (1-2 x)\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[(3 + 5*x)^2/(1 - 2*x),x]

[Out]

(-5*(-39 + 68*x + 20*x^2) - 242*Log[1 - 2*x])/16

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Maple [A]  time = 0.003, size = 18, normalized size = 0.8 \begin{align*} -{\frac{25\,{x}^{2}}{4}}-{\frac{85\,x}{4}}-{\frac{121\,\ln \left ( 2\,x-1 \right ) }{8}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25/4*x^2-85/4*x-121/8*ln(2*x-1)

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Maxima [A]  time = 0.988985, size = 23, normalized size = 1. \begin{align*} -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25/4*x^2 - 85/4*x - 121/8*log(2*x - 1)

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Fricas [A]  time = 1.28252, size = 55, normalized size = 2.39 \begin{align*} -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25/4*x^2 - 85/4*x - 121/8*log(2*x - 1)

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Sympy [A]  time = 0.080987, size = 22, normalized size = 0.96 \begin{align*} - \frac{25 x^{2}}{4} - \frac{85 x}{4} - \frac{121 \log{\left (2 x - 1 \right )}}{8} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25*x**2/4 - 85*x/4 - 121*log(2*x - 1)/8

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Giac [A]  time = 1.26556, size = 24, normalized size = 1.04 \begin{align*} -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25/4*x^2 - 85/4*x - 121/8*log(abs(2*x - 1))