3.1475 \(\int \frac{(3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=30 \[ -\frac{125 x^3}{6}-\frac{575 x^2}{8}-\frac{1115 x}{8}-\frac{1331}{16} \log (1-2 x) \]

[Out]

(-1115*x)/8 - (575*x^2)/8 - (125*x^3)/6 - (1331*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0102759, antiderivative size = 30, 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} \[ -\frac{125 x^3}{6}-\frac{575 x^2}{8}-\frac{1115 x}{8}-\frac{1331}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

Int[(3 + 5*x)^3/(1 - 2*x),x]

[Out]

(-1115*x)/8 - (575*x^2)/8 - (125*x^3)/6 - (1331*Log[1 - 2*x])/16

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)^3}{1-2 x} \, dx &=\int \left (-\frac{1115}{8}-\frac{575 x}{4}-\frac{125 x^2}{2}-\frac{1331}{8 (-1+2 x)}\right ) \, dx\\ &=-\frac{1115 x}{8}-\frac{575 x^2}{8}-\frac{125 x^3}{6}-\frac{1331}{16} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0074629, size = 30, normalized size = 1. \[ \frac{1}{96} \left (-5 \left (400 x^3+1380 x^2+2676 x-1733\right )-7986 \log (1-2 x)\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[(3 + 5*x)^3/(1 - 2*x),x]

[Out]

(-5*(-1733 + 2676*x + 1380*x^2 + 400*x^3) - 7986*Log[1 - 2*x])/96

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Maple [A]  time = 0.001, size = 23, normalized size = 0.8 \begin{align*} -{\frac{125\,{x}^{3}}{6}}-{\frac{575\,{x}^{2}}{8}}-{\frac{1115\,x}{8}}-{\frac{1331\,\ln \left ( 2\,x-1 \right ) }{16}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-125/6*x^3-575/8*x^2-1115/8*x-1331/16*ln(2*x-1)

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Maxima [A]  time = 1.06698, size = 30, normalized size = 1. \begin{align*} -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{16} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-125/6*x^3 - 575/8*x^2 - 1115/8*x - 1331/16*log(2*x - 1)

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Fricas [A]  time = 1.31803, size = 78, normalized size = 2.6 \begin{align*} -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{16} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-125/6*x^3 - 575/8*x^2 - 1115/8*x - 1331/16*log(2*x - 1)

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Sympy [A]  time = 0.0832, size = 29, normalized size = 0.97 \begin{align*} - \frac{125 x^{3}}{6} - \frac{575 x^{2}}{8} - \frac{1115 x}{8} - \frac{1331 \log{\left (2 x - 1 \right )}}{16} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-125*x**3/6 - 575*x**2/8 - 1115*x/8 - 1331*log(2*x - 1)/16

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Giac [A]  time = 2.30156, size = 31, normalized size = 1.03 \begin{align*} -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{16} \, \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)^3/(1-2*x),x, algorithm="giac")

[Out]

-125/6*x^3 - 575/8*x^2 - 1115/8*x - 1331/16*log(abs(2*x - 1))