Optimal. Leaf size=92 \[ -\frac{225}{64} (1-2 x)^{9/2}+\frac{13905}{224} (1-2 x)^{7/2}-\frac{159111}{320} (1-2 x)^{5/2}+\frac{40453}{16} (1-2 x)^{3/2}-\frac{832951}{64} \sqrt{1-2 x}-\frac{381073}{32 \sqrt{1-2 x}}+\frac{290521}{192 (1-2 x)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0808667, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{225}{64} (1-2 x)^{9/2}+\frac{13905}{224} (1-2 x)^{7/2}-\frac{159111}{320} (1-2 x)^{5/2}+\frac{40453}{16} (1-2 x)^{3/2}-\frac{832951}{64} \sqrt{1-2 x}-\frac{381073}{32 \sqrt{1-2 x}}+\frac{290521}{192 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 10.613, size = 82, normalized size = 0.89 \[ - \frac{225 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{13905 \left (- 2 x + 1\right )^{\frac{7}{2}}}{224} - \frac{159111 \left (- 2 x + 1\right )^{\frac{5}{2}}}{320} + \frac{40453 \left (- 2 x + 1\right )^{\frac{3}{2}}}{16} - \frac{832951 \sqrt{- 2 x + 1}}{64} - \frac{381073}{32 \sqrt{- 2 x + 1}} + \frac{290521}{192 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)**2/(1-2*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0563055, size = 43, normalized size = 0.47 \[ -\frac{23625 x^6+137700 x^5+402489 x^4+915492 x^3+3294996 x^2-6731112 x+2238664}{105 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{23625\,{x}^{6}+137700\,{x}^{5}+402489\,{x}^{4}+915492\,{x}^{3}+3294996\,{x}^{2}-6731112\,x+2238664}{105} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)^2/(1-2*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.35192, size = 81, normalized size = 0.88 \[ -\frac{225}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{13905}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{159111}{320} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{40453}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{832951}{64} \, \sqrt{-2 \, x + 1} + \frac{3773 \,{\left (1212 \, x - 529\right )}}{192 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219461, size = 62, normalized size = 0.67 \[ \frac{23625 \, x^{6} + 137700 \, x^{5} + 402489 \, x^{4} + 915492 \, x^{3} + 3294996 \, x^{2} - 6731112 \, x + 2238664}{105 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{4} \left (5 x + 3\right )^{2}}{\left (- 2 x + 1\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**4*(3+5*x)**2/(1-2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211987, size = 119, normalized size = 1.29 \[ -\frac{225}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{13905}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{159111}{320} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{40453}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{832951}{64} \, \sqrt{-2 \, x + 1} - \frac{3773 \,{\left (1212 \, x - 529\right )}}{192 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]