3.1396 \(\int \frac {(1-2 x)^3}{(2+3 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=37 \[ -\frac {8 x}{45}+\frac {343}{27 (3 x+2)}-\frac {1421}{27} \log (3 x+2)+\frac {1331}{25} \log (5 x+3) \]

[Out]

-8/45*x+343/27/(2+3*x)-1421/27*ln(2+3*x)+1331/25*ln(3+5*x)

________________________________________________________________________________________

Rubi [A]  time = 0.02, antiderivative size = 37, 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} \[ -\frac {8 x}{45}+\frac {343}{27 (3 x+2)}-\frac {1421}{27} \log (3 x+2)+\frac {1331}{25} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-8*x)/45 + 343/(27*(2 + 3*x)) - (1421*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/25

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 {(1-2 x)^3}{(2+3 x)^2 (3+5 x)} \, dx &=\int \left (-\frac {8}{45}-\frac {343}{9 (2+3 x)^2}-\frac {1421}{9 (2+3 x)}+\frac {1331}{5 (3+5 x)}\right ) \, dx\\ &=-\frac {8 x}{45}+\frac {343}{27 (2+3 x)}-\frac {1421}{27} \log (2+3 x)+\frac {1331}{25} \log (3+5 x)\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.03, size = 36, normalized size = 0.97 \[ \frac {1}{675} \left (-120 x+\frac {8575}{3 x+2}-35525 \log (5 (3 x+2))+35937 \log (5 x+3)-72\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-72 - 120*x + 8575/(2 + 3*x) - 35525*Log[5*(2 + 3*x)] + 35937*Log[3 + 5*x])/675

________________________________________________________________________________________

fricas [A]  time = 0.82, size = 45, normalized size = 1.22 \[ -\frac {360 \, x^{2} - 35937 \, {\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) + 35525 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 240 \, x - 8575}{675 \, {\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/675*(360*x^2 - 35937*(3*x + 2)*log(5*x + 3) + 35525*(3*x + 2)*log(3*x + 2) + 240*x - 8575)/(3*x + 2)

________________________________________________________________________________________

giac [A]  time = 0.93, size = 47, normalized size = 1.27 \[ -\frac {8}{45} \, x + \frac {343}{27 \, {\left (3 \, x + 2\right )}} - \frac {412}{675} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) + \frac {1331}{25} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {16}{135} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8/45*x + 343/27/(3*x + 2) - 412/675*log(1/3*abs(3*x + 2)/(3*x + 2)^2) + 1331/25*log(abs(-1/(3*x + 2) + 5)) -
16/135

________________________________________________________________________________________

maple [A]  time = 0.01, size = 30, normalized size = 0.81 \[ -\frac {8 x}{45}-\frac {1421 \ln \left (3 x +2\right )}{27}+\frac {1331 \ln \left (5 x +3\right )}{25}+\frac {343}{27 \left (3 x +2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8/45*x+343/27/(3*x+2)-1421/27*ln(3*x+2)+1331/25*ln(5*x+3)

________________________________________________________________________________________

maxima [A]  time = 0.59, size = 29, normalized size = 0.78 \[ -\frac {8}{45} \, x + \frac {343}{27 \, {\left (3 \, x + 2\right )}} + \frac {1331}{25} \, \log \left (5 \, x + 3\right ) - \frac {1421}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8/45*x + 343/27/(3*x + 2) + 1331/25*log(5*x + 3) - 1421/27*log(3*x + 2)

________________________________________________________________________________________

mupad [B]  time = 1.11, size = 25, normalized size = 0.68 \[ \frac {1331\,\ln \left (x+\frac {3}{5}\right )}{25}-\frac {1421\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {8\,x}{45}+\frac {343}{81\,\left (x+\frac {2}{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(1331*log(x + 3/5))/25 - (1421*log(x + 2/3))/27 - (8*x)/45 + 343/(81*(x + 2/3))

________________________________________________________________________________________

sympy [A]  time = 0.15, size = 31, normalized size = 0.84 \[ - \frac {8 x}{45} + \frac {1331 \log {\left (x + \frac {3}{5} \right )}}{25} - \frac {1421 \log {\left (x + \frac {2}{3} \right )}}{27} + \frac {343}{81 x + 54} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x/45 + 1331*log(x + 3/5)/25 - 1421*log(x + 2/3)/27 + 343/(81*x + 54)

________________________________________________________________________________________