3.1178 \(\int \frac{(1-2 x) (2+3 x)^4}{3+5 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{162 x^5}{25}-\frac{1269 x^4}{100}-\frac{531 x^3}{125}+\frac{7779 x^2}{1250}+\frac{16663 x}{3125}+\frac{11 \log (5 x+3)}{15625} \]

[Out]

(16663*x)/3125 + (7779*x^2)/1250 - (531*x^3)/125 - (1269*x^4)/100 - (162*x^5)/25
+ (11*Log[3 + 5*x])/15625

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Rubi [A]  time = 0.0422934, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{162 x^5}{25}-\frac{1269 x^4}{100}-\frac{531 x^3}{125}+\frac{7779 x^2}{1250}+\frac{16663 x}{3125}+\frac{11 \log (5 x+3)}{15625} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x),x]

[Out]

(16663*x)/3125 + (7779*x^2)/1250 - (531*x^3)/125 - (1269*x^4)/100 - (162*x^5)/25
+ (11*Log[3 + 5*x])/15625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{162 x^{5}}{25} - \frac{1269 x^{4}}{100} - \frac{531 x^{3}}{125} + \frac{11 \log{\left (5 x + 3 \right )}}{15625} + \int \frac{16663}{3125}\, dx + \frac{7779 \int x\, dx}{625} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**4/(3+5*x),x)

[Out]

-162*x**5/25 - 1269*x**4/100 - 531*x**3/125 + 11*log(5*x + 3)/15625 + Integral(1
6663/3125, x) + 7779*Integral(x, x)/625

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Mathematica [A]  time = 0.0218414, size = 37, normalized size = 0.84 \[ \frac{-2025000 x^5-3965625 x^4-1327500 x^3+1944750 x^2+1666300 x+220 \log (5 x+3)+369411}{312500} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x),x]

[Out]

(369411 + 1666300*x + 1944750*x^2 - 1327500*x^3 - 3965625*x^4 - 2025000*x^5 + 22
0*Log[3 + 5*x])/312500

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Maple [A]  time = 0.004, size = 33, normalized size = 0.8 \[{\frac{16663\,x}{3125}}+{\frac{7779\,{x}^{2}}{1250}}-{\frac{531\,{x}^{3}}{125}}-{\frac{1269\,{x}^{4}}{100}}-{\frac{162\,{x}^{5}}{25}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{15625}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^4/(3+5*x),x)

[Out]

16663/3125*x+7779/1250*x^2-531/125*x^3-1269/100*x^4-162/25*x^5+11/15625*ln(3+5*x
)

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Maxima [A]  time = 1.32388, size = 43, normalized size = 0.98 \[ -\frac{162}{25} \, x^{5} - \frac{1269}{100} \, x^{4} - \frac{531}{125} \, x^{3} + \frac{7779}{1250} \, x^{2} + \frac{16663}{3125} \, x + \frac{11}{15625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4*(2*x - 1)/(5*x + 3),x, algorithm="maxima")

[Out]

-162/25*x^5 - 1269/100*x^4 - 531/125*x^3 + 7779/1250*x^2 + 16663/3125*x + 11/156
25*log(5*x + 3)

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Fricas [A]  time = 0.203325, size = 43, normalized size = 0.98 \[ -\frac{162}{25} \, x^{5} - \frac{1269}{100} \, x^{4} - \frac{531}{125} \, x^{3} + \frac{7779}{1250} \, x^{2} + \frac{16663}{3125} \, x + \frac{11}{15625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4*(2*x - 1)/(5*x + 3),x, algorithm="fricas")

[Out]

-162/25*x^5 - 1269/100*x^4 - 531/125*x^3 + 7779/1250*x^2 + 16663/3125*x + 11/156
25*log(5*x + 3)

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Sympy [A]  time = 0.174901, size = 41, normalized size = 0.93 \[ - \frac{162 x^{5}}{25} - \frac{1269 x^{4}}{100} - \frac{531 x^{3}}{125} + \frac{7779 x^{2}}{1250} + \frac{16663 x}{3125} + \frac{11 \log{\left (5 x + 3 \right )}}{15625} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**4/(3+5*x),x)

[Out]

-162*x**5/25 - 1269*x**4/100 - 531*x**3/125 + 7779*x**2/1250 + 16663*x/3125 + 11
*log(5*x + 3)/15625

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GIAC/XCAS [A]  time = 0.207603, size = 45, normalized size = 1.02 \[ -\frac{162}{25} \, x^{5} - \frac{1269}{100} \, x^{4} - \frac{531}{125} \, x^{3} + \frac{7779}{1250} \, x^{2} + \frac{16663}{3125} \, x + \frac{11}{15625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4*(2*x - 1)/(5*x + 3),x, algorithm="giac")

[Out]

-162/25*x^5 - 1269/100*x^4 - 531/125*x^3 + 7779/1250*x^2 + 16663/3125*x + 11/156
25*ln(abs(5*x + 3))