3.11.41 \(\int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=49 \[ -\frac {3375 x^8}{4}-\frac {22275 x^7}{7}-\frac {9255 x^6}{2}-\frac {13943 x^5}{5}+\frac {883 x^4}{4}+1338 x^3+810 x^2+216 x \]

________________________________________________________________________________________

Rubi [A]  time = 0.02, antiderivative size = 49, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {3375 x^8}{4}-\frac {22275 x^7}{7}-\frac {9255 x^6}{2}-\frac {13943 x^5}{5}+\frac {883 x^4}{4}+1338 x^3+810 x^2+216 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275*x^7)/7 - (3375*x^8)/4

Rule 77

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*} \int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (216+1620 x+4014 x^2+883 x^3-13943 x^4-27765 x^5-22275 x^6-6750 x^7\right ) \, dx\\ &=216 x+810 x^2+1338 x^3+\frac {883 x^4}{4}-\frac {13943 x^5}{5}-\frac {9255 x^6}{2}-\frac {22275 x^7}{7}-\frac {3375 x^8}{4}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 49, normalized size = 1.00 \begin {gather*} -\frac {3375 x^8}{4}-\frac {22275 x^7}{7}-\frac {9255 x^6}{2}-\frac {13943 x^5}{5}+\frac {883 x^4}{4}+1338 x^3+810 x^2+216 x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275*x^7)/7 - (3375*x^8)/4

________________________________________________________________________________________

IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 1.34, size = 39, normalized size = 0.80 \begin {gather*} -\frac {3375}{4} x^{8} - \frac {22275}{7} x^{7} - \frac {9255}{2} x^{6} - \frac {13943}{5} x^{5} + \frac {883}{4} x^{4} + 1338 x^{3} + 810 x^{2} + 216 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 810*x^2 + 216*x

________________________________________________________________________________________

giac [A]  time = 1.24, size = 39, normalized size = 0.80 \begin {gather*} -\frac {3375}{4} \, x^{8} - \frac {22275}{7} \, x^{7} - \frac {9255}{2} \, x^{6} - \frac {13943}{5} \, x^{5} + \frac {883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 810*x^2 + 216*x

________________________________________________________________________________________

maple [A]  time = 0.00, size = 40, normalized size = 0.82 \begin {gather*} -\frac {3375}{4} x^{8}-\frac {22275}{7} x^{7}-\frac {9255}{2} x^{6}-\frac {13943}{5} x^{5}+\frac {883}{4} x^{4}+1338 x^{3}+810 x^{2}+216 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

216*x+810*x^2+1338*x^3+883/4*x^4-13943/5*x^5-9255/2*x^6-22275/7*x^7-3375/4*x^8

________________________________________________________________________________________

maxima [A]  time = 0.58, size = 39, normalized size = 0.80 \begin {gather*} -\frac {3375}{4} \, x^{8} - \frac {22275}{7} \, x^{7} - \frac {9255}{2} \, x^{6} - \frac {13943}{5} \, x^{5} + \frac {883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 810*x^2 + 216*x

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 39, normalized size = 0.80 \begin {gather*} -\frac {3375\,x^8}{4}-\frac {22275\,x^7}{7}-\frac {9255\,x^6}{2}-\frac {13943\,x^5}{5}+\frac {883\,x^4}{4}+1338\,x^3+810\,x^2+216\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275*x^7)/7 - (3375*x^8)/4

________________________________________________________________________________________

sympy [A]  time = 0.07, size = 46, normalized size = 0.94 \begin {gather*} - \frac {3375 x^{8}}{4} - \frac {22275 x^{7}}{7} - \frac {9255 x^{6}}{2} - \frac {13943 x^{5}}{5} + \frac {883 x^{4}}{4} + 1338 x^{3} + 810 x^{2} + 216 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375*x**8/4 - 22275*x**7/7 - 9255*x**6/2 - 13943*x**5/5 + 883*x**4/4 + 1338*x**3 + 810*x**2 + 216*x

________________________________________________________________________________________