Optimal. Leaf size=54 \[ \frac{376 (8 x+7)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 (2 x+3)^2 (35 x+29)}{3 \left (3 x^2+5 x+2\right )^{3/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0861762, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.074 \[ \frac{376 (8 x+7)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 (2 x+3)^2 (35 x+29)}{3 \left (3 x^2+5 x+2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^(5/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 13.4927, size = 48, normalized size = 0.89 \[ - \frac{2 \left (2 x + 3\right )^{2} \left (35 x + 29\right )}{3 \left (3 x^{2} + 5 x + 2\right )^{\frac{3}{2}}} + \frac{188 \left (16 x + 14\right )}{3 \sqrt{3 x^{2} + 5 x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3+2*x)**2/(3*x**2+5*x+2)**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0478535, size = 33, normalized size = 0.61 \[ \frac{2 \left (4372 x^3+10932 x^2+8925 x+2371\right )}{3 \left (3 x^2+5 x+2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^(5/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 38, normalized size = 0.7 \[{\frac{ \left ( 8744\,{x}^{3}+21864\,{x}^{2}+17850\,x+4742 \right ) \left ( 1+x \right ) \left ( 2+3\,x \right ) }{3} \left ( 3\,{x}^{2}+5\,x+2 \right ) ^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3+2*x)^2/(3*x^2+5*x+2)^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.714355, size = 103, normalized size = 1.91 \[ \frac{8744 \, x}{9 \, \sqrt{3 \, x^{2} + 5 \, x + 2}} + \frac{4 \, x^{2}}{3 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}}} + \frac{21860}{27 \, \sqrt{3 \, x^{2} + 5 \, x + 2}} - \frac{1114 \, x}{27 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}}} - \frac{1042}{27 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^2*(x - 5)/(3*x^2 + 5*x + 2)^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.272867, size = 69, normalized size = 1.28 \[ \frac{2 \,{\left (4372 \, x^{3} + 10932 \, x^{2} + 8925 \, x + 2371\right )} \sqrt{3 \, x^{2} + 5 \, x + 2}}{3 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^2*(x - 5)/(3*x^2 + 5*x + 2)^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \int \left (- \frac{51 x}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right )\, dx - \int \left (- \frac{8 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right )\, dx - \int \frac{4 x^{3}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left (- \frac{45}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3+2*x)**2/(3*x**2+5*x+2)**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.279135, size = 38, normalized size = 0.7 \[ \frac{2 \,{\left ({\left (4 \,{\left (1093 \, x + 2733\right )} x + 8925\right )} x + 2371\right )}}{3 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^2*(x - 5)/(3*x^2 + 5*x + 2)^(5/2),x, algorithm="giac")
[Out]