3.1238 \(\int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{100 (3 x+2)^{11}}{2673}-\frac{74}{243} (3 x+2)^{10}+\frac{503}{729} (3 x+2)^9-\frac{259}{972} (3 x+2)^8+\frac{7}{243} (3 x+2)^7 \]

[Out]

(7*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/972 + (503*(2 + 3*x)^9)/729 - (74*(2 + 3
*x)^10)/243 + (100*(2 + 3*x)^11)/2673

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Rubi [A]  time = 0.0956314, antiderivative size = 56, 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 \[ \frac{100 (3 x+2)^{11}}{2673}-\frac{74}{243} (3 x+2)^{10}+\frac{503}{729} (3 x+2)^9-\frac{259}{972} (3 x+2)^8+\frac{7}{243} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

(7*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/972 + (503*(2 + 3*x)^9)/729 - (74*(2 + 3
*x)^10)/243 + (100*(2 + 3*x)^11)/2673

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Rubi in Sympy [A]  time = 12.9946, size = 49, normalized size = 0.88 \[ \frac{100 \left (3 x + 2\right )^{11}}{2673} - \frac{74 \left (3 x + 2\right )^{10}}{243} + \frac{503 \left (3 x + 2\right )^{9}}{729} - \frac{259 \left (3 x + 2\right )^{8}}{972} + \frac{7 \left (3 x + 2\right )^{7}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**6*(3+5*x)**2,x)

[Out]

100*(3*x + 2)**11/2673 - 74*(3*x + 2)**10/243 + 503*(3*x + 2)**9/729 - 259*(3*x
+ 2)**8/972 + 7*(3*x + 2)**7/243

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Mathematica [A]  time = 0.00335502, size = 60, normalized size = 1.07 \[ \frac{72900 x^{11}}{11}+30618 x^{10}+55701 x^9+\frac{176391 x^8}{4}+675 x^7-26166 x^6-18340 x^5-1696 x^4+\frac{12208 x^3}{3}+2400 x^2+576 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

576*x + 2400*x^2 + (12208*x^3)/3 - 1696*x^4 - 18340*x^5 - 26166*x^6 + 675*x^7 +
(176391*x^8)/4 + 55701*x^9 + 30618*x^10 + (72900*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 1. \[{\frac{72900\,{x}^{11}}{11}}+30618\,{x}^{10}+55701\,{x}^{9}+{\frac{176391\,{x}^{8}}{4}}+675\,{x}^{7}-26166\,{x}^{6}-18340\,{x}^{5}-1696\,{x}^{4}+{\frac{12208\,{x}^{3}}{3}}+2400\,{x}^{2}+576\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x)

[Out]

72900/11*x^11+30618*x^10+55701*x^9+176391/4*x^8+675*x^7-26166*x^6-18340*x^5-1696
*x^4+12208/3*x^3+2400*x^2+576*x

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Maxima [A]  time = 1.34653, size = 73, normalized size = 1.3 \[ \frac{72900}{11} \, x^{11} + 30618 \, x^{10} + 55701 \, x^{9} + \frac{176391}{4} \, x^{8} + 675 \, x^{7} - 26166 \, x^{6} - 18340 \, x^{5} - 1696 \, x^{4} + \frac{12208}{3} \, x^{3} + 2400 \, x^{2} + 576 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^6*(2*x - 1)^2,x, algorithm="maxima")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18
340*x^5 - 1696*x^4 + 12208/3*x^3 + 2400*x^2 + 576*x

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Fricas [A]  time = 0.185378, size = 1, normalized size = 0.02 \[ \frac{72900}{11} x^{11} + 30618 x^{10} + 55701 x^{9} + \frac{176391}{4} x^{8} + 675 x^{7} - 26166 x^{6} - 18340 x^{5} - 1696 x^{4} + \frac{12208}{3} x^{3} + 2400 x^{2} + 576 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^6*(2*x - 1)^2,x, algorithm="fricas")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18
340*x^5 - 1696*x^4 + 12208/3*x^3 + 2400*x^2 + 576*x

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Sympy [A]  time = 0.111637, size = 58, normalized size = 1.04 \[ \frac{72900 x^{11}}{11} + 30618 x^{10} + 55701 x^{9} + \frac{176391 x^{8}}{4} + 675 x^{7} - 26166 x^{6} - 18340 x^{5} - 1696 x^{4} + \frac{12208 x^{3}}{3} + 2400 x^{2} + 576 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**6*(3+5*x)**2,x)

[Out]

72900*x**11/11 + 30618*x**10 + 55701*x**9 + 176391*x**8/4 + 675*x**7 - 26166*x**
6 - 18340*x**5 - 1696*x**4 + 12208*x**3/3 + 2400*x**2 + 576*x

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GIAC/XCAS [A]  time = 0.203257, size = 73, normalized size = 1.3 \[ \frac{72900}{11} \, x^{11} + 30618 \, x^{10} + 55701 \, x^{9} + \frac{176391}{4} \, x^{8} + 675 \, x^{7} - 26166 \, x^{6} - 18340 \, x^{5} - 1696 \, x^{4} + \frac{12208}{3} \, x^{3} + 2400 \, x^{2} + 576 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^6*(2*x - 1)^2,x, algorithm="giac")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18
340*x^5 - 1696*x^4 + 12208/3*x^3 + 2400*x^2 + 576*x