\(\int (1-2 x) (2+3 x)^8 (3+5 x) \, dx\) [1143]

Optimal result

Integrand size = 18, antiderivative size = 34 \[ \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx=-\frac {7}{243} (2+3 x)^9+\frac {37}{270} (2+3 x)^{10}-\frac {10}{297} (2+3 x)^{11} \]

[Out]

-7/243*(2+3*x)^9+37/270*(2+3*x)^10-10/297*(2+3*x)^11

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78} \[ \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx=-\frac {10}{297} (3 x+2)^{11}+\frac {37}{270} (3 x+2)^{10}-\frac {7}{243} (3 x+2)^9 \]

[In]

Int[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

(-7*(2 + 3*x)^9)/243 + (37*(2 + 3*x)^10)/270 - (10*(2 + 3*x)^11)/297

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 {7}{9} (2+3 x)^8+\frac {37}{9} (2+3 x)^9-\frac {10}{9} (2+3 x)^{10}\right ) \, dx \\ & = -\frac {7}{243} (2+3 x)^9+\frac {37}{270} (2+3 x)^{10}-\frac {10}{297} (2+3 x)^{11} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.82 \[ \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx=768 x+4480 x^2+\frac {42752 x^3}{3}+24576 x^4+\frac {62496 x^5}{5}-41328 x^6-110160 x^7-133164 x^8-92421 x^9-\frac {356481 x^{10}}{10}-\frac {65610 x^{11}}{11} \]

[In]

Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

768*x + 4480*x^2 + (42752*x^3)/3 + 24576*x^4 + (62496*x^5)/5 - 41328*x^6 - 110160*x^7 - 133164*x^8 - 92421*x^9
- (356481*x^10)/10 - (65610*x^11)/11

Maple [A] (verified)

Time = 2.11 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.59

method	result	size
gosper	\(-\frac {x \left (1968300 x^{10}[phone] x^{9}[phone] x^{8}[phone] x^{7}[phone] x^{6}[phone] x^{5}-4124736 x^{4}-8110080 x^{3}-4702720 x^{2}-1478400 x -253440\right )}{330}\)	\(54\)
default	\(-\frac {65610}{11} x^{11}-\frac {356481}{10} x^{10}-92421 x^{9}-133164 x^{8}-110160 x^{7}-41328 x^{6}+\frac {62496}{5} x^{5}+24576 x^{4}+\frac {42752}{3} x^{3}+4480 x^{2}+768 x\)	\(55\)
norman	\(-\frac {65610}{11} x^{11}-\frac {356481}{10} x^{10}-92421 x^{9}-133164 x^{8}-110160 x^{7}-41328 x^{6}+\frac {62496}{5} x^{5}+24576 x^{4}+\frac {42752}{3} x^{3}+4480 x^{2}+768 x\)	\(55\)
risch	\(-\frac {65610}{11} x^{11}-\frac {356481}{10} x^{10}-92421 x^{9}-133164 x^{8}-110160 x^{7}-41328 x^{6}+\frac {62496}{5} x^{5}+24576 x^{4}+\frac {42752}{3} x^{3}+4480 x^{2}+768 x\)	\(55\)
parallelrisch	\(-\frac {65610}{11} x^{11}-\frac {356481}{10} x^{10}-92421 x^{9}-133164 x^{8}-110160 x^{7}-41328 x^{6}+\frac {62496}{5} x^{5}+24576 x^{4}+\frac {42752}{3} x^{3}+4480 x^{2}+768 x\)	\(55\)

[In]

int((1-2*x)*(2+3*x)^8*(3+5*x),x,method=_RETURNVERBOSE)

[Out]

-1/330*x*(1968300*x^10+11763873*x^9+30498930*x^8+43944120*x^7+36352800*x^6+13638240*x^5-4124736*x^4-8110080*x^
3-4702720*x^2-1478400*x-253440)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.59 \[ \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx=-\frac {65610}{11} \, x^{11} - \frac {356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac {62496}{5} \, x^{5} + 24576 \, x^{4} + \frac {42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \]

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="fricas")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (29) = 58\).

Time = 0.03 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.76 \[ \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx=- \frac {65610 x^{11}}{11} - \frac {356481 x^{10}}{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac {62496 x^{5}}{5} + 24576 x^{4} + \frac {42752 x^{3}}{3} + 4480 x^{2} + 768 x \]

[In]

integrate((1-2*x)*(2+3*x)**8*(3+5*x),x)

[Out]

-65610*x**11/11 - 356481*x**10/10 - 92421*x**9 - 133164*x**8 - 110160*x**7 - 41328*x**6 + 62496*x**5/5 + 24576
*x**4 + 42752*x**3/3 + 4480*x**2 + 768*x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.59 \[ \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx=-\frac {65610}{11} \, x^{11} - \frac {356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac {62496}{5} \, x^{5} + 24576 \, x^{4} + \frac {42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \]

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="maxima")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.59 \[ \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx=-\frac {65610}{11} \, x^{11} - \frac {356481}{10} \, x^{10} - 92421 \, x^{9} - 133164 \, x^{8} - 110160 \, x^{7} - 41328 \, x^{6} + \frac {62496}{5} \, x^{5} + 24576 \, x^{4} + \frac {42752}{3} \, x^{3} + 4480 \, x^{2} + 768 \, x \]

[In]

integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm="giac")

[Out]

-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 +
42752/3*x^3 + 4480*x^2 + 768*x

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.59 \[ \int (1-2 x) (2+3 x)^8 (3+5 x) \, dx=-\frac {65610\,x^{11}}{11}-\frac {356481\,x^{10}}{10}-92421\,x^9-133164\,x^8-110160\,x^7-41328\,x^6+\frac {62496\,x^5}{5}+24576\,x^4+\frac {42752\,x^3}{3}+4480\,x^2+768\,x \]

[In]

int(-(2*x - 1)*(3*x + 2)^8*(5*x + 3),x)

[Out]

768*x + 4480*x^2 + (42752*x^3)/3 + 24576*x^4 + (62496*x^5)/5 - 41328*x^6 - 110160*x^7 - 133164*x^8 - 92421*x^9
- (356481*x^10)/10 - (65610*x^11)/11