3.14.48 \(\int \frac {(2+3 x)^6}{(1-2 x) (3+5 x)} \, dx\)

Optimal. Leaf size=54 \[ -\frac {729 x^5}{50}-\frac {28431 x^4}{400}-\frac {159813 x^3}{1000}-\frac {4693491 x^2}{20000}-\frac {31289679 x}{100000}-\frac {117649}{704} \log (1-2 x)+\frac {\log (5 x+3)}{171875} \]

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Rubi [A]  time = 0.02, antiderivative size = 54, 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 = {72} \begin {gather*} -\frac {729 x^5}{50}-\frac {28431 x^4}{400}-\frac {159813 x^3}{1000}-\frac {4693491 x^2}{20000}-\frac {31289679 x}{100000}-\frac {117649}{704} \log (1-2 x)+\frac {\log (5 x+3)}{171875} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)),x]

[Out]

(-31289679*x)/100000 - (4693491*x^2)/20000 - (159813*x^3)/1000 - (28431*x^4)/400 - (729*x^5)/50 - (117649*Log[
1 - 2*x])/704 + Log[3 + 5*x]/171875

Rule 72

Int[((e_.) + (f_.)*(x_))^(p_.)/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :> Int[ExpandIntegrand[(
e + f*x)^p/((a + b*x)*(c + d*x)), x], x] /; FreeQ[{a, b, c, d, e, f}, x] && IntegerQ[p]

Rubi steps

\begin {align*} \int \frac {(2+3 x)^6}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac {31289679}{100000}-\frac {4693491 x}{10000}-\frac {479439 x^2}{1000}-\frac {28431 x^3}{100}-\frac {729 x^4}{10}-\frac {117649}{352 (-1+2 x)}+\frac {1}{34375 (3+5 x)}\right ) \, dx\\ &=-\frac {31289679 x}{100000}-\frac {4693491 x^2}{20000}-\frac {159813 x^3}{1000}-\frac {28431 x^4}{400}-\frac {729 x^5}{50}-\frac {117649}{704} \log (1-2 x)+\frac {\log (3+5 x)}{171875}\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 50, normalized size = 0.93 \begin {gather*} \frac {-2970 \left (54000 x^5+263250 x^4+591900 x^3+869165 x^2+1158877 x+516778\right )-1838265625 \log (3-6 x)+64 \log (-3 (5 x+3))}{11000000} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)),x]

[Out]

(-2970*(516778 + 1158877*x + 869165*x^2 + 591900*x^3 + 263250*x^4 + 54000*x^5) - 1838265625*Log[3 - 6*x] + 64*
Log[-3*(3 + 5*x)])/11000000

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^6}{(1-2 x) (3+5 x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)),x]

[Out]

IntegrateAlgebraic[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)), x]

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fricas [A]  time = 0.90, size = 40, normalized size = 0.74 \begin {gather*} -\frac {729}{50} \, x^{5} - \frac {28431}{400} \, x^{4} - \frac {159813}{1000} \, x^{3} - \frac {4693491}{20000} \, x^{2} - \frac {31289679}{100000} \, x + \frac {1}{171875} \, \log \left (5 \, x + 3\right ) - \frac {117649}{704} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6/(1-2*x)/(3+5*x),x, algorithm="fricas")

[Out]

-729/50*x^5 - 28431/400*x^4 - 159813/1000*x^3 - 4693491/20000*x^2 - 31289679/100000*x + 1/171875*log(5*x + 3)
- 117649/704*log(2*x - 1)

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giac [A]  time = 1.02, size = 42, normalized size = 0.78 \begin {gather*} -\frac {729}{50} \, x^{5} - \frac {28431}{400} \, x^{4} - \frac {159813}{1000} \, x^{3} - \frac {4693491}{20000} \, x^{2} - \frac {31289679}{100000} \, x + \frac {1}{171875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {117649}{704} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6/(1-2*x)/(3+5*x),x, algorithm="giac")

[Out]

-729/50*x^5 - 28431/400*x^4 - 159813/1000*x^3 - 4693491/20000*x^2 - 31289679/100000*x + 1/171875*log(abs(5*x +
3)) - 117649/704*log(abs(2*x - 1))

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maple [A]  time = 0.01, size = 41, normalized size = 0.76 \begin {gather*} -\frac {729 x^{5}}{50}-\frac {28431 x^{4}}{400}-\frac {159813 x^{3}}{1000}-\frac {4693491 x^{2}}{20000}-\frac {31289679 x}{100000}-\frac {117649 \ln \left (2 x -1\right )}{704}+\frac {\ln \left (5 x +3\right )}{171875} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x+2)^6/(1-2*x)/(5*x+3),x)

[Out]

-729/50*x^5-28431/400*x^4-159813/1000*x^3-4693491/20000*x^2-31289679/100000*x+1/171875*ln(5*x+3)-117649/704*ln
(2*x-1)

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maxima [A]  time = 0.61, size = 40, normalized size = 0.74 \begin {gather*} -\frac {729}{50} \, x^{5} - \frac {28431}{400} \, x^{4} - \frac {159813}{1000} \, x^{3} - \frac {4693491}{20000} \, x^{2} - \frac {31289679}{100000} \, x + \frac {1}{171875} \, \log \left (5 \, x + 3\right ) - \frac {117649}{704} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6/(1-2*x)/(3+5*x),x, algorithm="maxima")

[Out]

-729/50*x^5 - 28431/400*x^4 - 159813/1000*x^3 - 4693491/20000*x^2 - 31289679/100000*x + 1/171875*log(5*x + 3)
- 117649/704*log(2*x - 1)

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mupad [B]  time = 1.12, size = 36, normalized size = 0.67 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{171875}-\frac {117649\,\ln \left (x-\frac {1}{2}\right )}{704}-\frac {31289679\,x}{100000}-\frac {4693491\,x^2}{20000}-\frac {159813\,x^3}{1000}-\frac {28431\,x^4}{400}-\frac {729\,x^5}{50} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*x + 2)^6/((2*x - 1)*(5*x + 3)),x)

[Out]

log(x + 3/5)/171875 - (117649*log(x - 1/2))/704 - (31289679*x)/100000 - (4693491*x^2)/20000 - (159813*x^3)/100
0 - (28431*x^4)/400 - (729*x^5)/50

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sympy [A]  time = 0.16, size = 49, normalized size = 0.91 \begin {gather*} - \frac {729 x^{5}}{50} - \frac {28431 x^{4}}{400} - \frac {159813 x^{3}}{1000} - \frac {4693491 x^{2}}{20000} - \frac {31289679 x}{100000} - \frac {117649 \log {\left (x - \frac {1}{2} \right )}}{704} + \frac {\log {\left (x + \frac {3}{5} \right )}}{171875} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**6/(1-2*x)/(3+5*x),x)

[Out]

-729*x**5/50 - 28431*x**4/400 - 159813*x**3/1000 - 4693491*x**2/20000 - 31289679*x/100000 - 117649*log(x - 1/2
)/704 + log(x + 3/5)/171875

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