3.1183 \(\int (1-2 x) (3+5 x)^3 \, dx\)

Optimal. Leaf size=23 \[ \frac{11}{100} (5 x+3)^4-\frac{2}{125} (5 x+3)^5 \]

[Out]

(11*(3 + 5*x)^4)/100 - (2*(3 + 5*x)^5)/125

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Rubi [A]  time = 0.0064627, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ \frac{11}{100} (5 x+3)^4-\frac{2}{125} (5 x+3)^5 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)*(3 + 5*x)^3,x]

[Out]

(11*(3 + 5*x)^4)/100 - (2*(3 + 5*x)^5)/125

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

\begin{align*} \int (1-2 x) (3+5 x)^3 \, dx &=\int \left (\frac{11}{5} (3+5 x)^3-\frac{2}{5} (3+5 x)^4\right ) \, dx\\ &=\frac{11}{100} (3+5 x)^4-\frac{2}{125} (3+5 x)^5\\ \end{align*}

Mathematica [A]  time = 0.0007083, size = 28, normalized size = 1.22 \[ -50 x^5-\frac{325 x^4}{4}-15 x^3+\frac{81 x^2}{2}+27 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)*(3 + 5*x)^3,x]

[Out]

27*x + (81*x^2)/2 - 15*x^3 - (325*x^4)/4 - 50*x^5

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Maple [A]  time = 0.001, size = 25, normalized size = 1.1 \begin{align*} -50\,{x}^{5}-{\frac{325\,{x}^{4}}{4}}-15\,{x}^{3}+{\frac{81\,{x}^{2}}{2}}+27\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-50*x^5-325/4*x^4-15*x^3+81/2*x^2+27*x

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Maxima [A]  time = 1.16429, size = 32, normalized size = 1.39 \begin{align*} -50 \, x^{5} - \frac{325}{4} \, x^{4} - 15 \, x^{3} + \frac{81}{2} \, x^{2} + 27 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-50*x^5 - 325/4*x^4 - 15*x^3 + 81/2*x^2 + 27*x

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Fricas [A]  time = 1.4937, size = 65, normalized size = 2.83 \begin{align*} -50 x^{5} - \frac{325}{4} x^{4} - 15 x^{3} + \frac{81}{2} x^{2} + 27 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-50*x^5 - 325/4*x^4 - 15*x^3 + 81/2*x^2 + 27*x

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Sympy [A]  time = 0.059436, size = 26, normalized size = 1.13 \begin{align*} - 50 x^{5} - \frac{325 x^{4}}{4} - 15 x^{3} + \frac{81 x^{2}}{2} + 27 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-50*x**5 - 325*x**4/4 - 15*x**3 + 81*x**2/2 + 27*x

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Giac [A]  time = 2.44256, size = 32, normalized size = 1.39 \begin{align*} -50 \, x^{5} - \frac{325}{4} \, x^{4} - 15 \, x^{3} + \frac{81}{2} \, x^{2} + 27 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-50*x^5 - 325/4*x^4 - 15*x^3 + 81/2*x^2 + 27*x