\(\int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx\) [1241]

Optimal result

Integrand size = 20, antiderivative size = 42 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx=24 x+26 x^2-\frac {154 x^3}{3}-\frac {425 x^4}{4}+\frac {99 x^5}{5}+144 x^6+\frac {540 x^7}{7} \]

[Out]

24*x+26*x^2-154/3*x^3-425/4*x^4+99/5*x^5+144*x^6+540/7*x^7

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 42, 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} \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx=\frac {540 x^7}{7}+144 x^6+\frac {99 x^5}{5}-\frac {425 x^4}{4}-\frac {154 x^3}{3}+26 x^2+24 x \]

[In]

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

[Out]

24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*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 (24+52 x-154 x^2-425 x^3+99 x^4+864 x^5+540 x^6\right ) \, dx \\ & = 24 x+26 x^2-\frac {154 x^3}{3}-\frac {425 x^4}{4}+\frac {99 x^5}{5}+144 x^6+\frac {540 x^7}{7} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx=24 x+26 x^2-\frac {154 x^3}{3}-\frac {425 x^4}{4}+\frac {99 x^5}{5}+144 x^6+\frac {540 x^7}{7} \]

[In]

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

[Out]

24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*x^7)/7

Maple [A] (verified)

Time = 1.84 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81

method	result	size
gosper	\(\frac {x \left (32400 x^{6}+60480 x^{5}+8316 x^{4}-44625 x^{3}-21560 x^{2}+10920 x +10080\right )}{420}\)	\(34\)
default	\(24 x +26 x^{2}-\frac {154}{3} x^{3}-\frac {425}{4} x^{4}+\frac {99}{5} x^{5}+144 x^{6}+\frac {540}{7} x^{7}\)	\(35\)
norman	\(24 x +26 x^{2}-\frac {154}{3} x^{3}-\frac {425}{4} x^{4}+\frac {99}{5} x^{5}+144 x^{6}+\frac {540}{7} x^{7}\)	\(35\)
risch	\(24 x +26 x^{2}-\frac {154}{3} x^{3}-\frac {425}{4} x^{4}+\frac {99}{5} x^{5}+144 x^{6}+\frac {540}{7} x^{7}\)	\(35\)
parallelrisch	\(24 x +26 x^{2}-\frac {154}{3} x^{3}-\frac {425}{4} x^{4}+\frac {99}{5} x^{5}+144 x^{6}+\frac {540}{7} x^{7}\)	\(35\)

[In]

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

[Out]

1/420*x*(32400*x^6+60480*x^5+8316*x^4-44625*x^3-21560*x^2+10920*x+10080)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx=\frac {540}{7} \, x^{7} + 144 \, x^{6} + \frac {99}{5} \, x^{5} - \frac {425}{4} \, x^{4} - \frac {154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \]

[In]

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

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.93 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx=\frac {540 x^{7}}{7} + 144 x^{6} + \frac {99 x^{5}}{5} - \frac {425 x^{4}}{4} - \frac {154 x^{3}}{3} + 26 x^{2} + 24 x \]

[In]

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

[Out]

540*x**7/7 + 144*x**6 + 99*x**5/5 - 425*x**4/4 - 154*x**3/3 + 26*x**2 + 24*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx=\frac {540}{7} \, x^{7} + 144 \, x^{6} + \frac {99}{5} \, x^{5} - \frac {425}{4} \, x^{4} - \frac {154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \]

[In]

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

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx=\frac {540}{7} \, x^{7} + 144 \, x^{6} + \frac {99}{5} \, x^{5} - \frac {425}{4} \, x^{4} - \frac {154}{3} \, x^{3} + 26 \, x^{2} + 24 \, x \]

[In]

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

[Out]

540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x) \, dx=\frac {540\,x^7}{7}+144\,x^6+\frac {99\,x^5}{5}-\frac {425\,x^4}{4}-\frac {154\,x^3}{3}+26\,x^2+24\,x \]

[In]

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

[Out]

24*x + 26*x^2 - (154*x^3)/3 - (425*x^4)/4 + (99*x^5)/5 + 144*x^6 + (540*x^7)/7