3.14.61 \(\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx\) [1361]

Optimal. Leaf size=47 \[ 36 x+6 x^2-\frac {395 x^3}{3}-57 x^4+\frac {1473 x^5}{5}+\frac {581 x^6}{3}-\frac {1860 x^7}{7}-225 x^8 \]

[Out]

36*x+6*x^2-395/3*x^3-57*x^4+1473/5*x^5+581/3*x^6-1860/7*x^7-225*x^8

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Rubi [A]
time = 0.01, antiderivative size = 47, 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*} -225 x^8-\frac {1860 x^7}{7}+\frac {581 x^6}{3}+\frac {1473 x^5}{5}-57 x^4-\frac {395 x^3}{3}+6 x^2+36 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7 - 225*x^8

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)^2 (3+5 x)^2 \, dx &=\int \left (36+12 x-395 x^2-228 x^3+1473 x^4+1162 x^5-1860 x^6-1800 x^7\right ) \, dx\\ &=36 x+6 x^2-\frac {395 x^3}{3}-57 x^4+\frac {1473 x^5}{5}+\frac {581 x^6}{3}-\frac {1860 x^7}{7}-225 x^8\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 47, normalized size = 1.00 \begin {gather*} 36 x+6 x^2-\frac {395 x^3}{3}-57 x^4+\frac {1473 x^5}{5}+\frac {581 x^6}{3}-\frac {1860 x^7}{7}-225 x^8 \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7 - 225*x^8

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Maple [A]
time = 0.10, size = 40, normalized size = 0.85

method	result	size
gosper	\(-\frac {x \left (23625 x^{7}+27900 x^{6}-20335 x^{5}-30933 x^{4}+5985 x^{3}+13825 x^{2}-630 x -3780\right )}{105}\)	\(39\)
default	\(36 x +6 x^{2}-\frac {395}{3} x^{3}-57 x^{4}+\frac {1473}{5} x^{5}+\frac {581}{3} x^{6}-\frac {1860}{7} x^{7}-225 x^{8}\)	\(40\)
norman	\(36 x +6 x^{2}-\frac {395}{3} x^{3}-57 x^{4}+\frac {1473}{5} x^{5}+\frac {581}{3} x^{6}-\frac {1860}{7} x^{7}-225 x^{8}\)	\(40\)
risch	\(36 x +6 x^{2}-\frac {395}{3} x^{3}-57 x^{4}+\frac {1473}{5} x^{5}+\frac {581}{3} x^{6}-\frac {1860}{7} x^{7}-225 x^{8}\)	\(40\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

36*x+6*x^2-395/3*x^3-57*x^4+1473/5*x^5+581/3*x^6-1860/7*x^7-225*x^8

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Maxima [A]
time = 0.44, size = 39, normalized size = 0.83 \begin {gather*} -225 \, x^{8} - \frac {1860}{7} \, x^{7} + \frac {581}{3} \, x^{6} + \frac {1473}{5} \, x^{5} - 57 \, x^{4} - \frac {395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36*x

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Fricas [A]
time = 0.38, size = 39, normalized size = 0.83 \begin {gather*} -225 \, x^{8} - \frac {1860}{7} \, x^{7} + \frac {581}{3} \, x^{6} + \frac {1473}{5} \, x^{5} - 57 \, x^{4} - \frac {395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36*x

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Sympy [A]
time = 0.02, size = 44, normalized size = 0.94 \begin {gather*} - 225 x^{8} - \frac {1860 x^{7}}{7} + \frac {581 x^{6}}{3} + \frac {1473 x^{5}}{5} - 57 x^{4} - \frac {395 x^{3}}{3} + 6 x^{2} + 36 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225*x**8 - 1860*x**7/7 + 581*x**6/3 + 1473*x**5/5 - 57*x**4 - 395*x**3/3 + 6*x**2 + 36*x

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Giac [A]
time = 4.06, size = 39, normalized size = 0.83 \begin {gather*} -225 \, x^{8} - \frac {1860}{7} \, x^{7} + \frac {581}{3} \, x^{6} + \frac {1473}{5} \, x^{5} - 57 \, x^{4} - \frac {395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36*x

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Mupad [B]
time = 0.03, size = 39, normalized size = 0.83 \begin {gather*} -225\,x^8-\frac {1860\,x^7}{7}+\frac {581\,x^6}{3}+\frac {1473\,x^5}{5}-57\,x^4-\frac {395\,x^3}{3}+6\,x^2+36\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7 - 225*x^8

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