\(\int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx\) [1344]

Optimal result

Integrand size = 20, antiderivative size = 40 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx=12 x-8 x^2-35 x^3+\frac {99 x^4}{4}+\frac {326 x^5}{5}-26 x^6-\frac {360 x^7}{7} \]

[Out]

12*x-8*x^2-35*x^3+99/4*x^4+326/5*x^5-26*x^6-360/7*x^7

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx=-\frac {360 x^7}{7}-26 x^6+\frac {326 x^5}{5}+\frac {99 x^4}{4}-35 x^3-8 x^2+12 x \]

[In]

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

Rule 78

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps \begin{align*} \text {integral}& = \int \left (12-16 x-105 x^2+99 x^3+326 x^4-156 x^5-360 x^6\right ) \, dx \\ & = 12 x-8 x^2-35 x^3+\frac {99 x^4}{4}+\frac {326 x^5}{5}-26 x^6-\frac {360 x^7}{7} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx=12 x-8 x^2-35 x^3+\frac {99 x^4}{4}+\frac {326 x^5}{5}-26 x^6-\frac {360 x^7}{7} \]

[In]

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7

Maple [A] (verified)

Time = 2.36 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85

method	result	size
gosper	\(-\frac {x \left (7200 x^{6}+3640 x^{5}-9128 x^{4}-3465 x^{3}+4900 x^{2}+1120 x -1680\right )}{140}\)	\(34\)
default	\(12 x -8 x^{2}-35 x^{3}+\frac {99}{4} x^{4}+\frac {326}{5} x^{5}-26 x^{6}-\frac {360}{7} x^{7}\)	\(35\)
norman	\(12 x -8 x^{2}-35 x^{3}+\frac {99}{4} x^{4}+\frac {326}{5} x^{5}-26 x^{6}-\frac {360}{7} x^{7}\)	\(35\)
risch	\(12 x -8 x^{2}-35 x^{3}+\frac {99}{4} x^{4}+\frac {326}{5} x^{5}-26 x^{6}-\frac {360}{7} x^{7}\)	\(35\)
parallelrisch	\(12 x -8 x^{2}-35 x^{3}+\frac {99}{4} x^{4}+\frac {326}{5} x^{5}-26 x^{6}-\frac {360}{7} x^{7}\)	\(35\)

[In]

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

[Out]

-1/140*x*(7200*x^6+3640*x^5-9128*x^4-3465*x^3+4900*x^2+1120*x-1680)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx=-\frac {360}{7} \, x^{7} - 26 \, x^{6} + \frac {326}{5} \, x^{5} + \frac {99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \]

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.92 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx=- \frac {360 x^{7}}{7} - 26 x^{6} + \frac {326 x^{5}}{5} + \frac {99 x^{4}}{4} - 35 x^{3} - 8 x^{2} + 12 x \]

[In]

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

[Out]

-360*x**7/7 - 26*x**6 + 326*x**5/5 + 99*x**4/4 - 35*x**3 - 8*x**2 + 12*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx=-\frac {360}{7} \, x^{7} - 26 \, x^{6} + \frac {326}{5} \, x^{5} + \frac {99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \]

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx=-\frac {360}{7} \, x^{7} - 26 \, x^{6} + \frac {326}{5} \, x^{5} + \frac {99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \]

[In]

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

[Out]

-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx=-\frac {360\,x^7}{7}-26\,x^6+\frac {326\,x^5}{5}+\frac {99\,x^4}{4}-35\,x^3-8\,x^2+12\,x \]

[In]

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

[Out]

12*x - 8*x^2 - 35*x^3 + (99*x^4)/4 + (326*x^5)/5 - 26*x^6 - (360*x^7)/7