3.1428 \(\int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=57 \[ \frac {1617}{3 x+2}+\frac {2541}{5 x+3}+\frac {343}{6 (3 x+2)^2}-\frac {1331}{10 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3) \]

[Out]

343/6/(2+3*x)^2+1617/(2+3*x)-1331/10/(3+5*x)^2+2541/(3+5*x)-15708*ln(2+3*x)+15708*ln(3+5*x)

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Rubi [A]  time = 0.03, antiderivative size = 57, 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} \[ \frac {1617}{3 x+2}+\frac {2541}{5 x+3}+\frac {343}{6 (3 x+2)^2}-\frac {1331}{10 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]

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

[Out]

343/(6*(2 + 3*x)^2) + 1617/(2 + 3*x) - 1331/(10*(3 + 5*x)^2) + 2541/(3 + 5*x) - 15708*Log[2 + 3*x] + 15708*Log
[3 + 5*x]

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)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {343}{(2+3 x)^3}-\frac {4851}{(2+3 x)^2}-\frac {47124}{2+3 x}+\frac {1331}{(3+5 x)^3}-\frac {12705}{(3+5 x)^2}+\frac {78540}{3+5 x}\right ) \, dx\\ &=\frac {343}{6 (2+3 x)^2}+\frac {1617}{2+3 x}-\frac {1331}{10 (3+5 x)^2}+\frac {2541}{3+5 x}-15708 \log (2+3 x)+15708 \log (3+5 x)\\ \end {align*}

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Mathematica [A]  time = 0.05, size = 59, normalized size = 1.04 \[ \frac {1617}{3 x+2}+\frac {2541}{5 x+3}+\frac {343}{6 (3 x+2)^2}-\frac {1331}{10 (5 x+3)^2}-15708 \log (5 (3 x+2))+15708 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]

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

[Out]

343/(6*(2 + 3*x)^2) + 1617/(2 + 3*x) - 1331/(10*(3 + 5*x)^2) + 2541/(3 + 5*x) - 15708*Log[5*(2 + 3*x)] + 15708
*Log[3 + 5*x]

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fricas [A]  time = 0.90, size = 95, normalized size = 1.67 \[ \frac {7068600 \, x^{3} + 13430348 \, x^{2} + 471240 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 471240 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 8492784 \, x + 1787403}{30 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/30*(7068600*x^3 + 13430348*x^2 + 471240*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(5*x + 3) - 471240*(22
5*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(3*x + 2) + 8492784*x + 1787403)/(225*x^4 + 570*x^3 + 541*x^2 + 228
*x + 36)

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giac [A]  time = 1.01, size = 48, normalized size = 0.84 \[ \frac {7068600 \, x^{3} + 13430348 \, x^{2} + 8492784 \, x + 1787403}{30 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 15708 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 15708 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/30*(7068600*x^3 + 13430348*x^2 + 8492784*x + 1787403)/(15*x^2 + 19*x + 6)^2 + 15708*log(abs(5*x + 3)) - 1570
8*log(abs(3*x + 2))

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maple [A]  time = 0.01, size = 54, normalized size = 0.95 \[ -15708 \ln \left (3 x +2\right )+15708 \ln \left (5 x +3\right )+\frac {343}{6 \left (3 x +2\right )^{2}}+\frac {1617}{3 x +2}-\frac {1331}{10 \left (5 x +3\right )^{2}}+\frac {2541}{5 x +3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

343/6/(3*x+2)^2+1617/(3*x+2)-1331/10/(5*x+3)^2+2541/(5*x+3)-15708*ln(3*x+2)+15708*ln(5*x+3)

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maxima [A]  time = 0.55, size = 56, normalized size = 0.98 \[ \frac {7068600 \, x^{3} + 13430348 \, x^{2} + 8492784 \, x + 1787403}{30 \, {\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 15708 \, \log \left (5 \, x + 3\right ) - 15708 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/30*(7068600*x^3 + 13430348*x^2 + 8492784*x + 1787403)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36) + 15708*log
(5*x + 3) - 15708*log(3*x + 2)

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mupad [B]  time = 1.13, size = 45, normalized size = 0.79 \[ \frac {\frac {5236\,x^3}{5}+\frac {6715174\,x^2}{3375}+\frac {1415464\,x}{1125}+\frac {595801}{2250}}{x^4+\frac {38\,x^3}{15}+\frac {541\,x^2}{225}+\frac {76\,x}{75}+\frac {4}{25}}-31416\,\mathrm {atanh}\left (30\,x+19\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((1415464*x)/1125 + (6715174*x^2)/3375 + (5236*x^3)/5 + 595801/2250)/((76*x)/75 + (541*x^2)/225 + (38*x^3)/15
+ x^4 + 4/25) - 31416*atanh(30*x + 19)

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sympy [A]  time = 0.18, size = 53, normalized size = 0.93 \[ - \frac {- 7068600 x^{3} - 13430348 x^{2} - 8492784 x - 1787403}{6750 x^{4} + 17100 x^{3} + 16230 x^{2} + 6840 x + 1080} + 15708 \log {\left (x + \frac {3}{5} \right )} - 15708 \log {\left (x + \frac {2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(-7068600*x**3 - 13430348*x**2 - 8492784*x - 1787403)/(6750*x**4 + 17100*x**3 + 16230*x**2 + 6840*x + 1080) +
15708*log(x + 3/5) - 15708*log(x + 2/3)

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