Optimal. Leaf size=72 \[ \frac{972 x^9}{5}+\frac{16767 x^8}{25}+\frac{672867 x^7}{875}+\frac{130383 x^6}{1250}-\frac{7315947 x^5}{15625}-\frac{20577159 x^4}{62500}+\frac{1327159 x^3}{78125}+\frac{80555569 x^2}{781250}+\frac{83333293 x}{1953125}+\frac{121 \log (5 x+3)}{9765625} \]
[Out]
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Rubi [A] time = 0.0719527, antiderivative size = 72, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{972 x^9}{5}+\frac{16767 x^8}{25}+\frac{672867 x^7}{875}+\frac{130383 x^6}{1250}-\frac{7315947 x^5}{15625}-\frac{20577159 x^4}{62500}+\frac{1327159 x^3}{78125}+\frac{80555569 x^2}{781250}+\frac{83333293 x}{1953125}+\frac{121 \log (5 x+3)}{9765625} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{972 x^{9}}{5} + \frac{16767 x^{8}}{25} + \frac{672867 x^{7}}{875} + \frac{130383 x^{6}}{1250} - \frac{7315947 x^{5}}{15625} - \frac{20577159 x^{4}}{62500} + \frac{1327159 x^{3}}{78125} + \frac{121 \log{\left (5 x + 3 \right )}}{9765625} + \int \frac{83333293}{1953125}\, dx + \frac{80555569 \int x\, dx}{390625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**7/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0237869, size = 57, normalized size = 0.79 \[ \frac{265781250000 x^9+916945312500 x^8+1051354687500 x^7+142606406250 x^6-640145362500 x^5-450125353125 x^4+23225282500 x^3+140972245750 x^2+58333305100 x+16940 \log (5 x+3)+7880238537}{1367187500} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x),x]
[Out]
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Maple [A] time = 0.006, size = 53, normalized size = 0.7 \[{\frac{83333293\,x}{1953125}}+{\frac{80555569\,{x}^{2}}{781250}}+{\frac{1327159\,{x}^{3}}{78125}}-{\frac{20577159\,{x}^{4}}{62500}}-{\frac{7315947\,{x}^{5}}{15625}}+{\frac{130383\,{x}^{6}}{1250}}+{\frac{672867\,{x}^{7}}{875}}+{\frac{16767\,{x}^{8}}{25}}+{\frac{972\,{x}^{9}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{9765625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^7/(3+5*x),x)
[Out]
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Maxima [A] time = 1.32422, size = 70, normalized size = 0.97 \[ \frac{972}{5} \, x^{9} + \frac{16767}{25} \, x^{8} + \frac{672867}{875} \, x^{7} + \frac{130383}{1250} \, x^{6} - \frac{7315947}{15625} \, x^{5} - \frac{20577159}{62500} \, x^{4} + \frac{1327159}{78125} \, x^{3} + \frac{80555569}{781250} \, x^{2} + \frac{83333293}{1953125} \, x + \frac{121}{9765625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^7*(2*x - 1)^2/(5*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213978, size = 70, normalized size = 0.97 \[ \frac{972}{5} \, x^{9} + \frac{16767}{25} \, x^{8} + \frac{672867}{875} \, x^{7} + \frac{130383}{1250} \, x^{6} - \frac{7315947}{15625} \, x^{5} - \frac{20577159}{62500} \, x^{4} + \frac{1327159}{78125} \, x^{3} + \frac{80555569}{781250} \, x^{2} + \frac{83333293}{1953125} \, x + \frac{121}{9765625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^7*(2*x - 1)^2/(5*x + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.207555, size = 68, normalized size = 0.94 \[ \frac{972 x^{9}}{5} + \frac{16767 x^{8}}{25} + \frac{672867 x^{7}}{875} + \frac{130383 x^{6}}{1250} - \frac{7315947 x^{5}}{15625} - \frac{20577159 x^{4}}{62500} + \frac{1327159 x^{3}}{78125} + \frac{80555569 x^{2}}{781250} + \frac{83333293 x}{1953125} + \frac{121 \log{\left (5 x + 3 \right )}}{9765625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**7/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.217317, size = 72, normalized size = 1. \[ \frac{972}{5} \, x^{9} + \frac{16767}{25} \, x^{8} + \frac{672867}{875} \, x^{7} + \frac{130383}{1250} \, x^{6} - \frac{7315947}{15625} \, x^{5} - \frac{20577159}{62500} \, x^{4} + \frac{1327159}{78125} \, x^{3} + \frac{80555569}{781250} \, x^{2} + \frac{83333293}{1953125} \, x + \frac{121}{9765625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^7*(2*x - 1)^2/(5*x + 3),x, algorithm="giac")
[Out]