3.13.59 \(\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^2 \, dx\) [1259]

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

[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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Rubi [A]
time = 0.01, antiderivative size = 42, normalized size of antiderivative = 1.00, 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 = {90} \begin {gather*} \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 {gather*}

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 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*} \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*}

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Mathematica [A]
time = 0.00, size = 42, normalized size = 1.00 \begin {gather*} 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 {gather*}

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 = 0.10, size = 35, normalized size = 0.83

method	result	size
gosper	\(\frac {x \left (27000 x^{6}+48300 x^{5}+4578 x^{4}-35805 x^{3}-15890 x^{2}+8820 x +7560\right )}{210}\)	\(34\)
default	\(36 x +42 x^{2}-\frac {227}{3} x^{3}-\frac {341}{2} x^{4}+\frac {109}{5} x^{5}+230 x^{6}+\frac {900}{7} x^{7}\)	\(35\)
norman	\(36 x +42 x^{2}-\frac {227}{3} x^{3}-\frac {341}{2} x^{4}+\frac {109}{5} x^{5}+230 x^{6}+\frac {900}{7} x^{7}\)	\(35\)
risch	\(36 x +42 x^{2}-\frac {227}{3} x^{3}-\frac {341}{2} x^{4}+\frac {109}{5} x^{5}+230 x^{6}+\frac {900}{7} x^{7}\)	\(35\)

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,method=_RETURNVERBOSE)

[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 = 0.31, size = 34, normalized size = 0.81 \begin {gather*} \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 {gather*}

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 = 0.40, size = 34, normalized size = 0.81 \begin {gather*} \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 {gather*}

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 = 0.01, size = 39, normalized size = 0.93 \begin {gather*} \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 {gather*}

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 = 0.57, size = 34, normalized size = 0.81 \begin {gather*} \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 {gather*}

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

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Mupad [B]
time = 0.02, size = 34, normalized size = 0.81 \begin {gather*} \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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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