3.1181 \(\int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx\)

Optimal. Leaf size=40 \[ -\frac{2250 x^7}{7}-\frac{1975 x^6}{2}-1061 x^5-\frac{1111 x^4}{4}+345 x^3+324 x^2+108 x \]

[Out]

108*x + 324*x^2 + 345*x^3 - (1111*x^4)/4 - 1061*x^5 - (1975*x^6)/2 - (2250*x^7)/7

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Rubi [A]  time = 0.0176297, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{2250 x^7}{7}-\frac{1975 x^6}{2}-1061 x^5-\frac{1111 x^4}{4}+345 x^3+324 x^2+108 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

108*x + 324*x^2 + 345*x^3 - (1111*x^4)/4 - 1061*x^5 - (1975*x^6)/2 - (2250*x^7)/7

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)^2 (3+5 x)^3 \, dx &=\int \left (108+648 x+1035 x^2-1111 x^3-5305 x^4-5925 x^5-2250 x^6\right ) \, dx\\ &=108 x+324 x^2+345 x^3-\frac{1111 x^4}{4}-1061 x^5-\frac{1975 x^6}{2}-\frac{2250 x^7}{7}\\ \end{align*}

Mathematica [A]  time = 0.0009116, size = 40, normalized size = 1. \[ -\frac{2250 x^7}{7}-\frac{1975 x^6}{2}-1061 x^5-\frac{1111 x^4}{4}+345 x^3+324 x^2+108 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

108*x + 324*x^2 + 345*x^3 - (1111*x^4)/4 - 1061*x^5 - (1975*x^6)/2 - (2250*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.9 \begin{align*} 108\,x+324\,{x}^{2}+345\,{x}^{3}-{\frac{1111\,{x}^{4}}{4}}-1061\,{x}^{5}-{\frac{1975\,{x}^{6}}{2}}-{\frac{2250\,{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

108*x+324*x^2+345*x^3-1111/4*x^4-1061*x^5-1975/2*x^6-2250/7*x^7

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Maxima [A]  time = 1.01578, size = 46, normalized size = 1.15 \begin{align*} -\frac{2250}{7} \, x^{7} - \frac{1975}{2} \, x^{6} - 1061 \, x^{5} - \frac{1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2250/7*x^7 - 1975/2*x^6 - 1061*x^5 - 1111/4*x^4 + 345*x^3 + 324*x^2 + 108*x

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Fricas [A]  time = 1.58774, size = 105, normalized size = 2.62 \begin{align*} -\frac{2250}{7} x^{7} - \frac{1975}{2} x^{6} - 1061 x^{5} - \frac{1111}{4} x^{4} + 345 x^{3} + 324 x^{2} + 108 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2250/7*x^7 - 1975/2*x^6 - 1061*x^5 - 1111/4*x^4 + 345*x^3 + 324*x^2 + 108*x

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Sympy [A]  time = 0.062326, size = 37, normalized size = 0.92 \begin{align*} - \frac{2250 x^{7}}{7} - \frac{1975 x^{6}}{2} - 1061 x^{5} - \frac{1111 x^{4}}{4} + 345 x^{3} + 324 x^{2} + 108 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2250*x**7/7 - 1975*x**6/2 - 1061*x**5 - 1111*x**4/4 + 345*x**3 + 324*x**2 + 108*x

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Giac [A]  time = 1.47852, size = 46, normalized size = 1.15 \begin{align*} -\frac{2250}{7} \, x^{7} - \frac{1975}{2} \, x^{6} - 1061 \, x^{5} - \frac{1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2250/7*x^7 - 1975/2*x^6 - 1061*x^5 - 1111/4*x^4 + 345*x^3 + 324*x^2 + 108*x