3.1259 \(\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=42 \[ \frac{900 x^7}{7}+230 x^6+\frac{109 x^5}{5}-\frac{341 x^4}{2}-\frac{227 x^3}{3}+42 x^2+36 x \]

[Out]

36*x + 42*x^2 - (227*x^3)/3 - (341*x^4)/2 + (109*x^5)/5 + 230*x^6 + (900*x^7)/7

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Rubi [A]  time = 0.0178049, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{900 x^7}{7}+230 x^6+\frac{109 x^5}{5}-\frac{341 x^4}{2}-\frac{227 x^3}{3}+42 x^2+36 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 42*x^2 - (227*x^3)/3 - (341*x^4)/2 + (109*x^5)/5 + 230*x^6 + (900*x^7)/7

Rule 88

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*} \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (36+84 x-227 x^2-682 x^3+109 x^4+1380 x^5+900 x^6\right ) \, dx\\ &=36 x+42 x^2-\frac{227 x^3}{3}-\frac{341 x^4}{2}+\frac{109 x^5}{5}+230 x^6+\frac{900 x^7}{7}\\ \end{align*}

Mathematica [A]  time = 0.0011879, size = 42, normalized size = 1. \[ \frac{900 x^7}{7}+230 x^6+\frac{109 x^5}{5}-\frac{341 x^4}{2}-\frac{227 x^3}{3}+42 x^2+36 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 42*x^2 - (227*x^3)/3 - (341*x^4)/2 + (109*x^5)/5 + 230*x^6 + (900*x^7)/7

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Maple [A]  time = 0.001, size = 35, normalized size = 0.8 \begin{align*} 36\,x+42\,{x}^{2}-{\frac{227\,{x}^{3}}{3}}-{\frac{341\,{x}^{4}}{2}}+{\frac{109\,{x}^{5}}{5}}+230\,{x}^{6}+{\frac{900\,{x}^{7}}{7}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

36*x+42*x^2-227/3*x^3-341/2*x^4+109/5*x^5+230*x^6+900/7*x^7

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Maxima [A]  time = 1.22729, size = 46, normalized size = 1.1 \begin{align*} \frac{900}{7} \, x^{7} + 230 \, x^{6} + \frac{109}{5} \, x^{5} - \frac{341}{2} \, x^{4} - \frac{227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

900/7*x^7 + 230*x^6 + 109/5*x^5 - 341/2*x^4 - 227/3*x^3 + 42*x^2 + 36*x

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Fricas [A]  time = 1.31159, size = 99, normalized size = 2.36 \begin{align*} \frac{900}{7} x^{7} + 230 x^{6} + \frac{109}{5} x^{5} - \frac{341}{2} x^{4} - \frac{227}{3} x^{3} + 42 x^{2} + 36 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

900/7*x^7 + 230*x^6 + 109/5*x^5 - 341/2*x^4 - 227/3*x^3 + 42*x^2 + 36*x

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Sympy [A]  time = 0.062157, size = 39, normalized size = 0.93 \begin{align*} \frac{900 x^{7}}{7} + 230 x^{6} + \frac{109 x^{5}}{5} - \frac{341 x^{4}}{2} - \frac{227 x^{3}}{3} + 42 x^{2} + 36 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

900*x**7/7 + 230*x**6 + 109*x**5/5 - 341*x**4/2 - 227*x**3/3 + 42*x**2 + 36*x

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Giac [A]  time = 1.775, size = 46, normalized size = 1.1 \begin{align*} \frac{900}{7} \, x^{7} + 230 \, x^{6} + \frac{109}{5} \, x^{5} - \frac{341}{2} \, x^{4} - \frac{227}{3} \, x^{3} + 42 \, x^{2} + 36 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

900/7*x^7 + 230*x^6 + 109/5*x^5 - 341/2*x^4 - 227/3*x^3 + 42*x^2 + 36*x