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

Optimal result

Integrand size = 22, antiderivative size = 47 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx=36 x+6 x^2-\frac {395 x^3}{3}-57 x^4+\frac {1473 x^5}{5}+\frac {581 x^6}{3}-\frac {1860 x^7}{7}-225 x^8 \]

[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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx=-225 x^8-\frac {1860 x^7}{7}+\frac {581 x^6}{3}+\frac {1473 x^5}{5}-57 x^4-\frac {395 x^3}{3}+6 x^2+36 x \]

[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*} \text {integral}& = \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*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx=36 x+6 x^2-\frac {395 x^3}{3}-57 x^4+\frac {1473 x^5}{5}+\frac {581 x^6}{3}-\frac {1860 x^7}{7}-225 x^8 \]

[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

Maple [A] (verified)

Time = 2.40 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83

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	\(36 x +6 x^{2}-\frac {395}{3} x^{3}-57 x^{4}+\frac {1473}{5} x^{5}+\frac {581}{3} x^{6}-\frac {1860}{7} x^{7}-225 x^{8}\)	\(40\)
parallelrisch	\(36 x +6 x^{2}-\frac {395}{3} x^{3}-57 x^{4}+\frac {1473}{5} x^{5}+\frac {581}{3} x^{6}-\frac {1860}{7} x^{7}-225 x^{8}\)	\(40\)

[In]

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

[Out]

-1/105*x*(23625*x^7+27900*x^6-20335*x^5-30933*x^4+5985*x^3+13825*x^2-630*x-3780)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx=-225 \, x^{8} - \frac {1860}{7} \, x^{7} + \frac {581}{3} \, x^{6} + \frac {1473}{5} \, x^{5} - 57 \, x^{4} - \frac {395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \]

[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

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.94 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx=- 225 x^{8} - \frac {1860 x^{7}}{7} + \frac {581 x^{6}}{3} + \frac {1473 x^{5}}{5} - 57 x^{4} - \frac {395 x^{3}}{3} + 6 x^{2} + 36 x \]

[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

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx=-225 \, x^{8} - \frac {1860}{7} \, x^{7} + \frac {581}{3} \, x^{6} + \frac {1473}{5} \, x^{5} - 57 \, x^{4} - \frac {395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \]

[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

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx=-225 \, x^{8} - \frac {1860}{7} \, x^{7} + \frac {581}{3} \, x^{6} + \frac {1473}{5} \, x^{5} - 57 \, x^{4} - \frac {395}{3} \, x^{3} + 6 \, x^{2} + 36 \, x \]

[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

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx=-225\,x^8-\frac {1860\,x^7}{7}+\frac {581\,x^6}{3}+\frac {1473\,x^5}{5}-57\,x^4-\frac {395\,x^3}{3}+6\,x^2+36\,x \]

[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