3.14.76 \(\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx\) [1376]

Optimal. Leaf size=59 \[ 216 x+378 x^2-534 x^3-\frac {8693 x^4}{4}-\frac {1419 x^5}{5}+\frac {10513 x^6}{2}+\frac {33013 x^7}{7}-\frac {14355 x^8}{4}-6900 x^9-2700 x^{10} \]

[Out]

216*x+378*x^2-534*x^3-8693/4*x^4-1419/5*x^5+10513/2*x^6+33013/7*x^7-14355/4*x^8-6900*x^9-2700*x^10

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Rubi [A]
time = 0.02, antiderivative size = 59, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \begin {gather*} -2700 x^{10}-6900 x^9-\frac {14355 x^8}{4}+\frac {33013 x^7}{7}+\frac {10513 x^6}{2}-\frac {1419 x^5}{5}-\frac {8693 x^4}{4}-534 x^3+378 x^2+216 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013*x^7)/7 - (14355*x^8)/4 - 6900
*x^9 - 2700*x^10

Rule 90

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin {align*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (216+756 x-1602 x^2-8693 x^3-1419 x^4+31539 x^5+33013 x^6-28710 x^7-62100 x^8-27000 x^9\right ) \, dx\\ &=216 x+378 x^2-534 x^3-\frac {8693 x^4}{4}-\frac {1419 x^5}{5}+\frac {10513 x^6}{2}+\frac {33013 x^7}{7}-\frac {14355 x^8}{4}-6900 x^9-2700 x^{10}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 59, normalized size = 1.00 \begin {gather*} 216 x+378 x^2-534 x^3-\frac {8693 x^4}{4}-\frac {1419 x^5}{5}+\frac {10513 x^6}{2}+\frac {33013 x^7}{7}-\frac {14355 x^8}{4}-6900 x^9-2700 x^{10} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013*x^7)/7 - (14355*x^8)/4 - 6900
*x^9 - 2700*x^10

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Maple [A]
time = 0.10, size = 50, normalized size = 0.85

method	result	size
gosper	\(-\frac {x \left (378000 x^{9}+966000 x^{8}+502425 x^{7}-660260 x^{6}-735910 x^{5}+39732 x^{4}+304255 x^{3}+74760 x^{2}-52920 x -30240\right )}{140}\)	\(49\)
default	\(216 x +378 x^{2}-534 x^{3}-\frac {8693}{4} x^{4}-\frac {1419}{5} x^{5}+\frac {10513}{2} x^{6}+\frac {33013}{7} x^{7}-\frac {14355}{4} x^{8}-6900 x^{9}-2700 x^{10}\)	\(50\)
norman	\(216 x +378 x^{2}-534 x^{3}-\frac {8693}{4} x^{4}-\frac {1419}{5} x^{5}+\frac {10513}{2} x^{6}+\frac {33013}{7} x^{7}-\frac {14355}{4} x^{8}-6900 x^{9}-2700 x^{10}\)	\(50\)
risch	\(216 x +378 x^{2}-534 x^{3}-\frac {8693}{4} x^{4}-\frac {1419}{5} x^{5}+\frac {10513}{2} x^{6}+\frac {33013}{7} x^{7}-\frac {14355}{4} x^{8}-6900 x^{9}-2700 x^{10}\)	\(50\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(2+3*x)^3*(3+5*x)^3,x,method=_RETURNVERBOSE)

[Out]

216*x+378*x^2-534*x^3-8693/4*x^4-1419/5*x^5+10513/2*x^6+33013/7*x^7-14355/4*x^8-6900*x^9-2700*x^10

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Maxima [A]
time = 0.28, size = 49, normalized size = 0.83 \begin {gather*} -2700 \, x^{10} - 6900 \, x^{9} - \frac {14355}{4} \, x^{8} + \frac {33013}{7} \, x^{7} + \frac {10513}{2} \, x^{6} - \frac {1419}{5} \, x^{5} - \frac {8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8693/4*x^4 - 534*x^3 + 378*x^2
+ 216*x

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Fricas [A]
time = 0.45, size = 49, normalized size = 0.83 \begin {gather*} -2700 \, x^{10} - 6900 \, x^{9} - \frac {14355}{4} \, x^{8} + \frac {33013}{7} \, x^{7} + \frac {10513}{2} \, x^{6} - \frac {1419}{5} \, x^{5} - \frac {8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8693/4*x^4 - 534*x^3 + 378*x^2
+ 216*x

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Sympy [A]
time = 0.03, size = 56, normalized size = 0.95 \begin {gather*} - 2700 x^{10} - 6900 x^{9} - \frac {14355 x^{8}}{4} + \frac {33013 x^{7}}{7} + \frac {10513 x^{6}}{2} - \frac {1419 x^{5}}{5} - \frac {8693 x^{4}}{4} - 534 x^{3} + 378 x^{2} + 216 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2700*x**10 - 6900*x**9 - 14355*x**8/4 + 33013*x**7/7 + 10513*x**6/2 - 1419*x**5/5 - 8693*x**4/4 - 534*x**3 +
378*x**2 + 216*x

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Giac [A]
time = 1.09, size = 49, normalized size = 0.83 \begin {gather*} -2700 \, x^{10} - 6900 \, x^{9} - \frac {14355}{4} \, x^{8} + \frac {33013}{7} \, x^{7} + \frac {10513}{2} \, x^{6} - \frac {1419}{5} \, x^{5} - \frac {8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8693/4*x^4 - 534*x^3 + 378*x^2
+ 216*x

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Mupad [B]
time = 0.04, size = 49, normalized size = 0.83 \begin {gather*} -2700\,x^{10}-6900\,x^9-\frac {14355\,x^8}{4}+\frac {33013\,x^7}{7}+\frac {10513\,x^6}{2}-\frac {1419\,x^5}{5}-\frac {8693\,x^4}{4}-534\,x^3+378\,x^2+216\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013*x^7)/7 - (14355*x^8)/4 - 6900
*x^9 - 2700*x^10

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