\(\int (1-2 x)^3 (3+5 x)^3 \, dx\) [1379]

Optimal result

Integrand size = 15, antiderivative size = 40 \[ \int (1-2 x)^3 (3+5 x)^3 \, dx=27 x-\frac {27 x^2}{2}-87 x^3+\frac {179 x^4}{4}+174 x^5-50 x^6-\frac {1000 x^7}{7} \]

[Out]

27*x-27/2*x^2-87*x^3+179/4*x^4+174*x^5-50*x^6-1000/7*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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45} \[ \int (1-2 x)^3 (3+5 x)^3 \, dx=-\frac {1000 x^7}{7}-50 x^6+174 x^5+\frac {179 x^4}{4}-87 x^3-\frac {27 x^2}{2}+27 x \]

[In]

Int[(1 - 2*x)^3*(3 + 5*x)^3,x]

[Out]

27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps \begin{align*} \text {integral}& = \int \left (27-27 x-261 x^2+179 x^3+870 x^4-300 x^5-1000 x^6\right ) \, dx \\ & = 27 x-\frac {27 x^2}{2}-87 x^3+\frac {179 x^4}{4}+174 x^5-50 x^6-\frac {1000 x^7}{7} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (3+5 x)^3 \, dx=27 x-\frac {27 x^2}{2}-87 x^3+\frac {179 x^4}{4}+174 x^5-50 x^6-\frac {1000 x^7}{7} \]

[In]

Integrate[(1 - 2*x)^3*(3 + 5*x)^3,x]

[Out]

27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7

Maple [A] (verified)

Time = 2.40 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85

method	result	size
gosper	\(-\frac {x \left (4000 x^{6}+1400 x^{5}-4872 x^{4}-1253 x^{3}+2436 x^{2}+378 x -756\right )}{28}\)	\(34\)
default	\(27 x -\frac {27}{2} x^{2}-87 x^{3}+\frac {179}{4} x^{4}+174 x^{5}-50 x^{6}-\frac {1000}{7} x^{7}\)	\(35\)
norman	\(27 x -\frac {27}{2} x^{2}-87 x^{3}+\frac {179}{4} x^{4}+174 x^{5}-50 x^{6}-\frac {1000}{7} x^{7}\)	\(35\)
risch	\(27 x -\frac {27}{2} x^{2}-87 x^{3}+\frac {179}{4} x^{4}+174 x^{5}-50 x^{6}-\frac {1000}{7} x^{7}\)	\(35\)
parallelrisch	\(27 x -\frac {27}{2} x^{2}-87 x^{3}+\frac {179}{4} x^{4}+174 x^{5}-50 x^{6}-\frac {1000}{7} x^{7}\)	\(35\)

[In]

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

[Out]

-1/28*x*(4000*x^6+1400*x^5-4872*x^4-1253*x^3+2436*x^2+378*x-756)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^3 (3+5 x)^3 \, dx=-\frac {1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac {179}{4} \, x^{4} - 87 \, x^{3} - \frac {27}{2} \, x^{2} + 27 \, x \]

[In]

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.92 \[ \int (1-2 x)^3 (3+5 x)^3 \, dx=- \frac {1000 x^{7}}{7} - 50 x^{6} + 174 x^{5} + \frac {179 x^{4}}{4} - 87 x^{3} - \frac {27 x^{2}}{2} + 27 x \]

[In]

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

[Out]

-1000*x**7/7 - 50*x**6 + 174*x**5 + 179*x**4/4 - 87*x**3 - 27*x**2/2 + 27*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^3 (3+5 x)^3 \, dx=-\frac {1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac {179}{4} \, x^{4} - 87 \, x^{3} - \frac {27}{2} \, x^{2} + 27 \, x \]

[In]

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^3 (3+5 x)^3 \, dx=-\frac {1000}{7} \, x^{7} - 50 \, x^{6} + 174 \, x^{5} + \frac {179}{4} \, x^{4} - 87 \, x^{3} - \frac {27}{2} \, x^{2} + 27 \, x \]

[In]

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

[Out]

-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^3 (3+5 x)^3 \, dx=-\frac {1000\,x^7}{7}-50\,x^6+174\,x^5+\frac {179\,x^4}{4}-87\,x^3-\frac {27\,x^2}{2}+27\,x \]

[In]

int(-(2*x - 1)^3*(5*x + 3)^3,x)

[Out]

27*x - (27*x^2)/2 - 87*x^3 + (179*x^4)/4 + 174*x^5 - 50*x^6 - (1000*x^7)/7