\(\int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx\) [1255]

Optimal result

Integrand size = 22, antiderivative size = 56 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx=\frac {7}{243} (2+3 x)^7-\frac {259}{972} (2+3 x)^8+\frac {503}{729} (2+3 x)^9-\frac {74}{243} (2+3 x)^{10}+\frac {100 (2+3 x)^{11}}{2673} \]

[Out]

7/243*(2+3*x)^7-259/972*(2+3*x)^8+503/729*(2+3*x)^9-74/243*(2+3*x)^10+100/2673*(2+3*x)^11

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, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx=\frac {100 (3 x+2)^{11}}{2673}-\frac {74}{243} (3 x+2)^{10}+\frac {503}{729} (3 x+2)^9-\frac {259}{972} (3 x+2)^8+\frac {7}{243} (3 x+2)^7 \]

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

(7*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/972 + (503*(2 + 3*x)^9)/729 - (74*(2 + 3*x)^10)/243 + (100*(2 + 3*x)^1
1)/2673

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 (\frac {49}{81} (2+3 x)^6-\frac {518}{81} (2+3 x)^7+\frac {503}{27} (2+3 x)^8-\frac {740}{81} (2+3 x)^9+\frac {100}{81} (2+3 x)^{10}\right ) \, dx \\ & = \frac {7}{243} (2+3 x)^7-\frac {259}{972} (2+3 x)^8+\frac {503}{729} (2+3 x)^9-\frac {74}{243} (2+3 x)^{10}+\frac {100 (2+3 x)^{11}}{2673} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.07 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx=576 x+2400 x^2+\frac {12208 x^3}{3}-1696 x^4-18340 x^5-26166 x^6+675 x^7+\frac {176391 x^8}{4}+55701 x^9+30618 x^{10}+\frac {72900 x^{11}}{11} \]

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

576*x + 2400*x^2 + (12208*x^3)/3 - 1696*x^4 - 18340*x^5 - 26166*x^6 + 675*x^7 + (176391*x^8)/4 + 55701*x^9 + 3
0618*x^10 + (72900*x^11)/11

Maple [A] (verified)

Time = 2.27 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96

method	result	size
gosper	\(\frac {x \left (874800 x^{10}+4041576 x^{9}+7352532 x^{8}+5820903 x^{7}+89100 x^{6}-3453912 x^{5}-2420880 x^{4}-223872 x^{3}+537152 x^{2}+316800 x +76032\right )}{132}\)	\(54\)
default	\(\frac {72900}{11} x^{11}+30618 x^{10}+55701 x^{9}+\frac {176391}{4} x^{8}+675 x^{7}-26166 x^{6}-18340 x^{5}-1696 x^{4}+\frac {12208}{3} x^{3}+2400 x^{2}+576 x\)	\(55\)
norman	\(\frac {72900}{11} x^{11}+30618 x^{10}+55701 x^{9}+\frac {176391}{4} x^{8}+675 x^{7}-26166 x^{6}-18340 x^{5}-1696 x^{4}+\frac {12208}{3} x^{3}+2400 x^{2}+576 x\)	\(55\)
risch	\(\frac {72900}{11} x^{11}+30618 x^{10}+55701 x^{9}+\frac {176391}{4} x^{8}+675 x^{7}-26166 x^{6}-18340 x^{5}-1696 x^{4}+\frac {12208}{3} x^{3}+2400 x^{2}+576 x\)	\(55\)
parallelrisch	\(\frac {72900}{11} x^{11}+30618 x^{10}+55701 x^{9}+\frac {176391}{4} x^{8}+675 x^{7}-26166 x^{6}-18340 x^{5}-1696 x^{4}+\frac {12208}{3} x^{3}+2400 x^{2}+576 x\)	\(55\)

[In]

int((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x,method=_RETURNVERBOSE)

[Out]

1/132*x*(874800*x^10+4041576*x^9+7352532*x^8+5820903*x^7+89100*x^6-3453912*x^5-2420880*x^4-223872*x^3+537152*x
^2+316800*x+76032)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx=\frac {72900}{11} \, x^{11} + 30618 \, x^{10} + 55701 \, x^{9} + \frac {176391}{4} \, x^{8} + 675 \, x^{7} - 26166 \, x^{6} - 18340 \, x^{5} - 1696 \, x^{4} + \frac {12208}{3} \, x^{3} + 2400 \, x^{2} + 576 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x, algorithm="fricas")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18340*x^5 - 1696*x^4 + 12208/3*x
^3 + 2400*x^2 + 576*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.04 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx=\frac {72900 x^{11}}{11} + 30618 x^{10} + 55701 x^{9} + \frac {176391 x^{8}}{4} + 675 x^{7} - 26166 x^{6} - 18340 x^{5} - 1696 x^{4} + \frac {12208 x^{3}}{3} + 2400 x^{2} + 576 x \]

[In]

integrate((1-2*x)**2*(2+3*x)**6*(3+5*x)**2,x)

[Out]

72900*x**11/11 + 30618*x**10 + 55701*x**9 + 176391*x**8/4 + 675*x**7 - 26166*x**6 - 18340*x**5 - 1696*x**4 + 1
2208*x**3/3 + 2400*x**2 + 576*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx=\frac {72900}{11} \, x^{11} + 30618 \, x^{10} + 55701 \, x^{9} + \frac {176391}{4} \, x^{8} + 675 \, x^{7} - 26166 \, x^{6} - 18340 \, x^{5} - 1696 \, x^{4} + \frac {12208}{3} \, x^{3} + 2400 \, x^{2} + 576 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x, algorithm="maxima")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18340*x^5 - 1696*x^4 + 12208/3*x
^3 + 2400*x^2 + 576*x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx=\frac {72900}{11} \, x^{11} + 30618 \, x^{10} + 55701 \, x^{9} + \frac {176391}{4} \, x^{8} + 675 \, x^{7} - 26166 \, x^{6} - 18340 \, x^{5} - 1696 \, x^{4} + \frac {12208}{3} \, x^{3} + 2400 \, x^{2} + 576 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x, algorithm="giac")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18340*x^5 - 1696*x^4 + 12208/3*x
^3 + 2400*x^2 + 576*x

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx=\frac {72900\,x^{11}}{11}+30618\,x^{10}+55701\,x^9+\frac {176391\,x^8}{4}+675\,x^7-26166\,x^6-18340\,x^5-1696\,x^4+\frac {12208\,x^3}{3}+2400\,x^2+576\,x \]

[In]

int((2*x - 1)^2*(3*x + 2)^6*(5*x + 3)^2,x)

[Out]

576*x + 2400*x^2 + (12208*x^3)/3 - 1696*x^4 - 18340*x^5 - 26166*x^6 + 675*x^7 + (176391*x^8)/4 + 55701*x^9 + 3
0618*x^10 + (72900*x^11)/11