\(\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx\) [1258]

Optimal result

Integrand size = 22, antiderivative size = 51 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx=72 x+138 x^2-\frac {202 x^3}{3}-\frac {2045 x^4}{4}-\frac {1828 x^5}{5}+\frac {1029 x^6}{2}+\frac {5940 x^7}{7}+\frac {675 x^8}{2} \]

[Out]

72*x+138*x^2-202/3*x^3-2045/4*x^4-1828/5*x^5+1029/2*x^6+5940/7*x^7+675/2*x^8

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 51, 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} \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx=\frac {675 x^8}{2}+\frac {5940 x^7}{7}+\frac {1029 x^6}{2}-\frac {1828 x^5}{5}-\frac {2045 x^4}{4}-\frac {202 x^3}{3}+138 x^2+72 x \]

[In]

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

[Out]

72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (5940*x^7)/7 + (675*x^8)/2

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 (72+276 x-202 x^2-2045 x^3-1828 x^4+3087 x^5+5940 x^6+2700 x^7\right ) \, dx \\ & = 72 x+138 x^2-\frac {202 x^3}{3}-\frac {2045 x^4}{4}-\frac {1828 x^5}{5}+\frac {1029 x^6}{2}+\frac {5940 x^7}{7}+\frac {675 x^8}{2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx=72 x+138 x^2-\frac {202 x^3}{3}-\frac {2045 x^4}{4}-\frac {1828 x^5}{5}+\frac {1029 x^6}{2}+\frac {5940 x^7}{7}+\frac {675 x^8}{2} \]

[In]

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

[Out]

72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (5940*x^7)/7 + (675*x^8)/2

Maple [A] (verified)

Time = 2.27 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.76

method	result	size
gosper	\(\frac {x \left (141750 x^{7}+356400 x^{6}+216090 x^{5}-153552 x^{4}-214725 x^{3}-28280 x^{2}+57960 x +30240\right )}{420}\)	\(39\)
default	\(72 x +138 x^{2}-\frac {202}{3} x^{3}-\frac {2045}{4} x^{4}-\frac {1828}{5} x^{5}+\frac {1029}{2} x^{6}+\frac {5940}{7} x^{7}+\frac {675}{2} x^{8}\)	\(40\)
norman	\(72 x +138 x^{2}-\frac {202}{3} x^{3}-\frac {2045}{4} x^{4}-\frac {1828}{5} x^{5}+\frac {1029}{2} x^{6}+\frac {5940}{7} x^{7}+\frac {675}{2} x^{8}\)	\(40\)
risch	\(72 x +138 x^{2}-\frac {202}{3} x^{3}-\frac {2045}{4} x^{4}-\frac {1828}{5} x^{5}+\frac {1029}{2} x^{6}+\frac {5940}{7} x^{7}+\frac {675}{2} x^{8}\)	\(40\)
parallelrisch	\(72 x +138 x^{2}-\frac {202}{3} x^{3}-\frac {2045}{4} x^{4}-\frac {1828}{5} x^{5}+\frac {1029}{2} x^{6}+\frac {5940}{7} x^{7}+\frac {675}{2} x^{8}\)	\(40\)

[In]

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

[Out]

1/420*x*(141750*x^7+356400*x^6+216090*x^5-153552*x^4-214725*x^3-28280*x^2+57960*x+30240)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.76 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx=\frac {675}{2} \, x^{8} + \frac {5940}{7} \, x^{7} + \frac {1029}{2} \, x^{6} - \frac {1828}{5} \, x^{5} - \frac {2045}{4} \, x^{4} - \frac {202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \]

[In]

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*x^2 + 72*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.94 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx=\frac {675 x^{8}}{2} + \frac {5940 x^{7}}{7} + \frac {1029 x^{6}}{2} - \frac {1828 x^{5}}{5} - \frac {2045 x^{4}}{4} - \frac {202 x^{3}}{3} + 138 x^{2} + 72 x \]

[In]

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

[Out]

675*x**8/2 + 5940*x**7/7 + 1029*x**6/2 - 1828*x**5/5 - 2045*x**4/4 - 202*x**3/3 + 138*x**2 + 72*x

Maxima [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.76 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx=\frac {675}{2} \, x^{8} + \frac {5940}{7} \, x^{7} + \frac {1029}{2} \, x^{6} - \frac {1828}{5} \, x^{5} - \frac {2045}{4} \, x^{4} - \frac {202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \]

[In]

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*x^2 + 72*x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.76 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx=\frac {675}{2} \, x^{8} + \frac {5940}{7} \, x^{7} + \frac {1029}{2} \, x^{6} - \frac {1828}{5} \, x^{5} - \frac {2045}{4} \, x^{4} - \frac {202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \]

[In]

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*x^2 + 72*x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.76 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx=\frac {675\,x^8}{2}+\frac {5940\,x^7}{7}+\frac {1029\,x^6}{2}-\frac {1828\,x^5}{5}-\frac {2045\,x^4}{4}-\frac {202\,x^3}{3}+138\,x^2+72\,x \]

[In]

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

[Out]

72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (5940*x^7)/7 + (675*x^8)/2