\(\int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx\) [1341]

Optimal result

Integrand size = 20, antiderivative size = 56 \[ \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx=-\frac {343 (2+3 x)^6}{1458}+\frac {287}{243} (2+3 x)^7-\frac {259}{324} (2+3 x)^8+\frac {428 (2+3 x)^9}{2187}-\frac {4}{243} (2+3 x)^{10} \]

[Out]

-343/1458*(2+3*x)^6+287/243*(2+3*x)^7-259/324*(2+3*x)^8+428/2187*(2+3*x)^9-4/243*(2+3*x)^10

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 56, 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} \[ \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx=-\frac {4}{243} (3 x+2)^{10}+\frac {428 (3 x+2)^9}{2187}-\frac {259}{324} (3 x+2)^8+\frac {287}{243} (3 x+2)^7-\frac {343 (3 x+2)^6}{1458} \]

[In]

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

[Out]

(-343*(2 + 3*x)^6)/1458 + (287*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/324 + (428*(2 + 3*x)^9)/2187 - (4*(2 + 3*x
)^10)/243

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 (-\frac {343}{81} (2+3 x)^5+\frac {2009}{81} (2+3 x)^6-\frac {518}{27} (2+3 x)^7+\frac {428}{81} (2+3 x)^8-\frac {40}{81} (2+3 x)^9\right ) \, dx \\ & = -\frac {343 (2+3 x)^6}{1458}+\frac {287}{243} (2+3 x)^7-\frac {259}{324} (2+3 x)^8+\frac {428 (2+3 x)^9}{2187}-\frac {4}{243} (2+3 x)^{10} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.95 \[ \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx=96 x+152 x^2-256 x^3-882 x^4+14 x^5+\frac {4333 x^6}{2}+1683 x^7-\frac {6291 x^8}{4}-2628 x^9-972 x^{10} \]

[In]

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

[Out]

96*x + 152*x^2 - 256*x^3 - 882*x^4 + 14*x^5 + (4333*x^6)/2 + 1683*x^7 - (6291*x^8)/4 - 2628*x^9 - 972*x^10

Maple [A] (verified)

Time = 2.36 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88

method	result	size
gosper	\(-\frac {x \left (3888 x^{9}+10512 x^{8}+6291 x^{7}-6732 x^{6}-8666 x^{5}-56 x^{4}+3528 x^{3}+1024 x^{2}-608 x -384\right )}{4}\)	\(49\)
default	\(-972 x^{10}-2628 x^{9}-\frac {6291}{4} x^{8}+1683 x^{7}+\frac {4333}{2} x^{6}+14 x^{5}-882 x^{4}-256 x^{3}+152 x^{2}+96 x\)	\(50\)
norman	\(-972 x^{10}-2628 x^{9}-\frac {6291}{4} x^{8}+1683 x^{7}+\frac {4333}{2} x^{6}+14 x^{5}-882 x^{4}-256 x^{3}+152 x^{2}+96 x\)	\(50\)
risch	\(-972 x^{10}-2628 x^{9}-\frac {6291}{4} x^{8}+1683 x^{7}+\frac {4333}{2} x^{6}+14 x^{5}-882 x^{4}-256 x^{3}+152 x^{2}+96 x\)	\(50\)
parallelrisch	\(-972 x^{10}-2628 x^{9}-\frac {6291}{4} x^{8}+1683 x^{7}+\frac {4333}{2} x^{6}+14 x^{5}-882 x^{4}-256 x^{3}+152 x^{2}+96 x\)	\(50\)

[In]

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

[Out]

-1/4*x*(3888*x^9+10512*x^8+6291*x^7-6732*x^6-8666*x^5-56*x^4+3528*x^3+1024*x^2-608*x-384)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx=-972 \, x^{10} - 2628 \, x^{9} - \frac {6291}{4} \, x^{8} + 1683 \, x^{7} + \frac {4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \]

[In]

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 256*x^3 + 152*x^2 + 96*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.91 \[ \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx=- 972 x^{10} - 2628 x^{9} - \frac {6291 x^{8}}{4} + 1683 x^{7} + \frac {4333 x^{6}}{2} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x \]

[In]

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

[Out]

-972*x**10 - 2628*x**9 - 6291*x**8/4 + 1683*x**7 + 4333*x**6/2 + 14*x**5 - 882*x**4 - 256*x**3 + 152*x**2 + 96
*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx=-972 \, x^{10} - 2628 \, x^{9} - \frac {6291}{4} \, x^{8} + 1683 \, x^{7} + \frac {4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \]

[In]

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 256*x^3 + 152*x^2 + 96*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx=-972 \, x^{10} - 2628 \, x^{9} - \frac {6291}{4} \, x^{8} + 1683 \, x^{7} + \frac {4333}{2} \, x^{6} + 14 \, x^{5} - 882 \, x^{4} - 256 \, x^{3} + 152 \, x^{2} + 96 \, x \]

[In]

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

[Out]

-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 256*x^3 + 152*x^2 + 96*x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^5 (3+5 x) \, dx=-972\,x^{10}-2628\,x^9-\frac {6291\,x^8}{4}+1683\,x^7+\frac {4333\,x^6}{2}+14\,x^5-882\,x^4-256\,x^3+152\,x^2+96\,x \]

[In]

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

[Out]

96*x + 152*x^2 - 256*x^3 - 882*x^4 + 14*x^5 + (4333*x^6)/2 + 1683*x^7 - (6291*x^8)/4 - 2628*x^9 - 972*x^10