3.1129 \(\int (1-2 x) (2+3 x)^5 (3+5 x) \, dx\)

Optimal. Leaf size=34 \[ -\frac{5}{108} (3 x+2)^8+\frac{37}{189} (3 x+2)^7-\frac{7}{162} (3 x+2)^6 \]

[Out]

(-7*(2 + 3*x)^6)/162 + (37*(2 + 3*x)^7)/189 - (5*(2 + 3*x)^8)/108

_______________________________________________________________________________________

Rubi [A]  time = 0.0561433, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{5}{108} (3 x+2)^8+\frac{37}{189} (3 x+2)^7-\frac{7}{162} (3 x+2)^6 \]

Antiderivative was successfully verified.

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

[Out]

(-7*(2 + 3*x)^6)/162 + (37*(2 + 3*x)^7)/189 - (5*(2 + 3*x)^8)/108

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 8.27254, size = 29, normalized size = 0.85 \[ - \frac{5 \left (3 x + 2\right )^{8}}{108} + \frac{37 \left (3 x + 2\right )^{7}}{189} - \frac{7 \left (3 x + 2\right )^{6}}{162} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5*(3*x + 2)**8/108 + 37*(3*x + 2)**7/189 - 7*(3*x + 2)**6/162

_______________________________________________________________________________________

Mathematica [A]  time = 0.00314831, size = 47, normalized size = 1.38 \[ -\frac{1215 x^8}{4}-\frac{8343 x^7}{7}-\frac{3627 x^6}{2}-1170 x^5+30 x^4+\frac{1600 x^3}{3}+344 x^2+96 x \]

Antiderivative was successfully verified.

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

[Out]

96*x + 344*x^2 + (1600*x^3)/3 + 30*x^4 - 1170*x^5 - (3627*x^6)/2 - (8343*x^7)/7
- (1215*x^8)/4

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 40, normalized size = 1.2 \[ -{\frac{1215\,{x}^{8}}{4}}-{\frac{8343\,{x}^{7}}{7}}-{\frac{3627\,{x}^{6}}{2}}-1170\,{x}^{5}+30\,{x}^{4}+{\frac{1600\,{x}^{3}}{3}}+344\,{x}^{2}+96\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215/4*x^8-8343/7*x^7-3627/2*x^6-1170*x^5+30*x^4+1600/3*x^3+344*x^2+96*x

_______________________________________________________________________________________

Maxima [A]  time = 1.32222, size = 53, normalized size = 1.56 \[ -\frac{1215}{4} \, x^{8} - \frac{8343}{7} \, x^{7} - \frac{3627}{2} \, x^{6} - 1170 \, x^{5} + 30 \, x^{4} + \frac{1600}{3} \, x^{3} + 344 \, x^{2} + 96 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215/4*x^8 - 8343/7*x^7 - 3627/2*x^6 - 1170*x^5 + 30*x^4 + 1600/3*x^3 + 344*x^2
+ 96*x

_______________________________________________________________________________________

Fricas [A]  time = 0.190539, size = 1, normalized size = 0.03 \[ -\frac{1215}{4} x^{8} - \frac{8343}{7} x^{7} - \frac{3627}{2} x^{6} - 1170 x^{5} + 30 x^{4} + \frac{1600}{3} x^{3} + 344 x^{2} + 96 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215/4*x^8 - 8343/7*x^7 - 3627/2*x^6 - 1170*x^5 + 30*x^4 + 1600/3*x^3 + 344*x^2
+ 96*x

_______________________________________________________________________________________

Sympy [A]  time = 0.088878, size = 44, normalized size = 1.29 \[ - \frac{1215 x^{8}}{4} - \frac{8343 x^{7}}{7} - \frac{3627 x^{6}}{2} - 1170 x^{5} + 30 x^{4} + \frac{1600 x^{3}}{3} + 344 x^{2} + 96 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215*x**8/4 - 8343*x**7/7 - 3627*x**6/2 - 1170*x**5 + 30*x**4 + 1600*x**3/3 + 3
44*x**2 + 96*x

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.216593, size = 53, normalized size = 1.56 \[ -\frac{1215}{4} \, x^{8} - \frac{8343}{7} \, x^{7} - \frac{3627}{2} \, x^{6} - 1170 \, x^{5} + 30 \, x^{4} + \frac{1600}{3} \, x^{3} + 344 \, x^{2} + 96 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1215/4*x^8 - 8343/7*x^7 - 3627/2*x^6 - 1170*x^5 + 30*x^4 + 1600/3*x^3 + 344*x^2
+ 96*x