\(\int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx\) [1362]

Optimal result

Integrand size = 20, antiderivative size = 46 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx=18 x-\frac {21 x^2}{2}-\frac {166 x^3}{3}+\frac {135 x^4}{4}+\frac {534 x^5}{5}-\frac {110 x^6}{3}-\frac {600 x^7}{7} \]

[Out]

18*x-21/2*x^2-166/3*x^3+135/4*x^4+534/5*x^5-110/3*x^6-600/7*x^7

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 46, 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} \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx=-\frac {600 x^7}{7}-\frac {110 x^6}{3}+\frac {534 x^5}{5}+\frac {135 x^4}{4}-\frac {166 x^3}{3}-\frac {21 x^2}{2}+18 x \]

[In]

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*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 (18-21 x-166 x^2+135 x^3+534 x^4-220 x^5-600 x^6\right ) \, dx \\ & = 18 x-\frac {21 x^2}{2}-\frac {166 x^3}{3}+\frac {135 x^4}{4}+\frac {534 x^5}{5}-\frac {110 x^6}{3}-\frac {600 x^7}{7} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx=18 x-\frac {21 x^2}{2}-\frac {166 x^3}{3}+\frac {135 x^4}{4}+\frac {534 x^5}{5}-\frac {110 x^6}{3}-\frac {600 x^7}{7} \]

[In]

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*x^7)/7

Maple [A] (verified)

Time = 2.41 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.74

method	result	size
gosper	\(-\frac {x \left (36000 x^{6}+15400 x^{5}-44856 x^{4}-14175 x^{3}+23240 x^{2}+4410 x -7560\right )}{420}\)	\(34\)
default	\(18 x -\frac {21}{2} x^{2}-\frac {166}{3} x^{3}+\frac {135}{4} x^{4}+\frac {534}{5} x^{5}-\frac {110}{3} x^{6}-\frac {600}{7} x^{7}\)	\(35\)
norman	\(18 x -\frac {21}{2} x^{2}-\frac {166}{3} x^{3}+\frac {135}{4} x^{4}+\frac {534}{5} x^{5}-\frac {110}{3} x^{6}-\frac {600}{7} x^{7}\)	\(35\)
risch	\(18 x -\frac {21}{2} x^{2}-\frac {166}{3} x^{3}+\frac {135}{4} x^{4}+\frac {534}{5} x^{5}-\frac {110}{3} x^{6}-\frac {600}{7} x^{7}\)	\(35\)
parallelrisch	\(18 x -\frac {21}{2} x^{2}-\frac {166}{3} x^{3}+\frac {135}{4} x^{4}+\frac {534}{5} x^{5}-\frac {110}{3} x^{6}-\frac {600}{7} x^{7}\)	\(35\)

[In]

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

[Out]

-1/420*x*(36000*x^6+15400*x^5-44856*x^4-14175*x^3+23240*x^2+4410*x-7560)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.74 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx=-\frac {600}{7} \, x^{7} - \frac {110}{3} \, x^{6} + \frac {534}{5} \, x^{5} + \frac {135}{4} \, x^{4} - \frac {166}{3} \, x^{3} - \frac {21}{2} \, x^{2} + 18 \, x \]

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.91 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx=- \frac {600 x^{7}}{7} - \frac {110 x^{6}}{3} + \frac {534 x^{5}}{5} + \frac {135 x^{4}}{4} - \frac {166 x^{3}}{3} - \frac {21 x^{2}}{2} + 18 x \]

[In]

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

[Out]

-600*x**7/7 - 110*x**6/3 + 534*x**5/5 + 135*x**4/4 - 166*x**3/3 - 21*x**2/2 + 18*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.74 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx=-\frac {600}{7} \, x^{7} - \frac {110}{3} \, x^{6} + \frac {534}{5} \, x^{5} + \frac {135}{4} \, x^{4} - \frac {166}{3} \, x^{3} - \frac {21}{2} \, x^{2} + 18 \, x \]

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.74 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx=-\frac {600}{7} \, x^{7} - \frac {110}{3} \, x^{6} + \frac {534}{5} \, x^{5} + \frac {135}{4} \, x^{4} - \frac {166}{3} \, x^{3} - \frac {21}{2} \, x^{2} + 18 \, x \]

[In]

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

[Out]

-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.74 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx=-\frac {600\,x^7}{7}-\frac {110\,x^6}{3}+\frac {534\,x^5}{5}+\frac {135\,x^4}{4}-\frac {166\,x^3}{3}-\frac {21\,x^2}{2}+18\,x \]

[In]

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

[Out]

18*x - (21*x^2)/2 - (166*x^3)/3 + (135*x^4)/4 + (534*x^5)/5 - (110*x^6)/3 - (600*x^7)/7