3.14.75 \(\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^3 \, dx\) [1375]

Optimal. Leaf size=62 \[ 432 x+1080 x^2-312 x^3-5548 x^4-\frac {28917 x^5}{5}+\frac {19607 x^6}{2}+22949 x^7+\frac {41619 x^8}{8}-23370 x^9-24030 x^{10}-\frac {81000 x^{11}}{11} \]

[Out]

432*x+1080*x^2-312*x^3-5548*x^4-28917/5*x^5+19607/2*x^6+22949*x^7+41619/8*x^8-23370*x^9-24030*x^10-81000/11*x^
11

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Rubi [A]
time = 0.02, antiderivative size = 62, 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*} -\frac {81000 x^{11}}{11}-24030 x^{10}-23370 x^9+\frac {41619 x^8}{8}+22949 x^7+\frac {19607 x^6}{2}-\frac {28917 x^5}{5}-5548 x^4-312 x^3+1080 x^2+432 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^7 + (41619*x^8)/8 - 23370*x^9
- 24030*x^10 - (81000*x^11)/11

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)^4 (3+5 x)^3 \, dx &=\int \left (432+2160 x-936 x^2-22192 x^3-28917 x^4+58821 x^5+160643 x^6+41619 x^7-210330 x^8-240300 x^9-81000 x^{10}\right ) \, dx\\ &=432 x+1080 x^2-312 x^3-5548 x^4-\frac {28917 x^5}{5}+\frac {19607 x^6}{2}+22949 x^7+\frac {41619 x^8}{8}-23370 x^9-24030 x^{10}-\frac {81000 x^{11}}{11}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 62, normalized size = 1.00 \begin {gather*} 432 x+1080 x^2-312 x^3-5548 x^4-\frac {28917 x^5}{5}+\frac {19607 x^6}{2}+22949 x^7+\frac {41619 x^8}{8}-23370 x^9-24030 x^{10}-\frac {81000 x^{11}}{11} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^7 + (41619*x^8)/8 - 23370*x^9
- 24030*x^10 - (81000*x^11)/11

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Maple [A]
time = 0.08, size = 55, normalized size = 0.89

method	result	size
gosper	\(-\frac {x \left (3240000 x^{10}[phone] x^{9}[phone] x^{8}-2289045 x^{7}-10097560 x^{6}-4313540 x^{5}+2544696 x^{4}+2441120 x^{3}+137280 x^{2}-475200 x -190080\right )}{440}\)	\(54\)
default	\(432 x +1080 x^{2}-312 x^{3}-5548 x^{4}-\frac {28917}{5} x^{5}+\frac {19607}{2} x^{6}+22949 x^{7}+\frac {41619}{8} x^{8}-23370 x^{9}-24030 x^{10}-\frac {81000}{11} x^{11}\)	\(55\)
norman	\(432 x +1080 x^{2}-312 x^{3}-5548 x^{4}-\frac {28917}{5} x^{5}+\frac {19607}{2} x^{6}+22949 x^{7}+\frac {41619}{8} x^{8}-23370 x^{9}-24030 x^{10}-\frac {81000}{11} x^{11}\)	\(55\)
risch	\(432 x +1080 x^{2}-312 x^{3}-5548 x^{4}-\frac {28917}{5} x^{5}+\frac {19607}{2} x^{6}+22949 x^{7}+\frac {41619}{8} x^{8}-23370 x^{9}-24030 x^{10}-\frac {81000}{11} x^{11}\)	\(55\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x,method=_RETURNVERBOSE)

[Out]

432*x+1080*x^2-312*x^3-5548*x^4-28917/5*x^5+19607/2*x^6+22949*x^7+41619/8*x^8-23370*x^9-24030*x^10-81000/11*x^
11

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Maxima [A]
time = 0.28, size = 54, normalized size = 0.87 \begin {gather*} -\frac {81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac {41619}{8} \, x^{8} + 22949 \, x^{7} + \frac {19607}{2} \, x^{6} - \frac {28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x, algorithm="maxima")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6 - 28917/5*x^5 - 5548*x^4 - 312
*x^3 + 1080*x^2 + 432*x

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Fricas [A]
time = 0.44, size = 54, normalized size = 0.87 \begin {gather*} -\frac {81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac {41619}{8} \, x^{8} + 22949 \, x^{7} + \frac {19607}{2} \, x^{6} - \frac {28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x, algorithm="fricas")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6 - 28917/5*x^5 - 5548*x^4 - 312
*x^3 + 1080*x^2 + 432*x

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Sympy [A]
time = 0.01, size = 60, normalized size = 0.97 \begin {gather*} - \frac {81000 x^{11}}{11} - 24030 x^{10} - 23370 x^{9} + \frac {41619 x^{8}}{8} + 22949 x^{7} + \frac {19607 x^{6}}{2} - \frac {28917 x^{5}}{5} - 5548 x^{4} - 312 x^{3} + 1080 x^{2} + 432 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**3,x)

[Out]

-81000*x**11/11 - 24030*x**10 - 23370*x**9 + 41619*x**8/8 + 22949*x**7 + 19607*x**6/2 - 28917*x**5/5 - 5548*x*
*4 - 312*x**3 + 1080*x**2 + 432*x

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Giac [A]
time = 0.94, size = 54, normalized size = 0.87 \begin {gather*} -\frac {81000}{11} \, x^{11} - 24030 \, x^{10} - 23370 \, x^{9} + \frac {41619}{8} \, x^{8} + 22949 \, x^{7} + \frac {19607}{2} \, x^{6} - \frac {28917}{5} \, x^{5} - 5548 \, x^{4} - 312 \, x^{3} + 1080 \, x^{2} + 432 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x, algorithm="giac")

[Out]

-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6 - 28917/5*x^5 - 5548*x^4 - 312
*x^3 + 1080*x^2 + 432*x

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Mupad [B]
time = 0.06, size = 54, normalized size = 0.87 \begin {gather*} -\frac {81000\,x^{11}}{11}-24030\,x^{10}-23370\,x^9+\frac {41619\,x^8}{8}+22949\,x^7+\frac {19607\,x^6}{2}-\frac {28917\,x^5}{5}-5548\,x^4-312\,x^3+1080\,x^2+432\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)^3*(3*x + 2)^4*(5*x + 3)^3,x)

[Out]

432*x + 1080*x^2 - 312*x^3 - 5548*x^4 - (28917*x^5)/5 + (19607*x^6)/2 + 22949*x^7 + (41619*x^8)/8 - 23370*x^9
- 24030*x^10 - (81000*x^11)/11

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