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

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

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Rubi [A]  time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {11}{100} (5 x+3)^4-\frac {2}{125} (5 x+3)^5 \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 28, normalized size = 1.22 \begin {gather*} -50 x^5-\frac {325 x^4}{4}-15 x^3+\frac {81 x^2}{2}+27 x \end {gather*}

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

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.09, size = 24, normalized size = 1.04 \begin {gather*} -50 x^{5} - \frac {325}{4} x^{4} - 15 x^{3} + \frac {81}{2} x^{2} + 27 x \end {gather*}

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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giac [A]  time = 1.19, size = 24, normalized size = 1.04 \begin {gather*} -50 \, x^{5} - \frac {325}{4} \, x^{4} - 15 \, x^{3} + \frac {81}{2} \, x^{2} + 27 \, x \end {gather*}

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

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maple [A]  time = 0.00, size = 25, normalized size = 1.09 \begin {gather*} -50 x^{5}-\frac {325}{4} x^{4}-15 x^{3}+\frac {81}{2} x^{2}+27 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)*(5*x+3)^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 = 0.43, size = 24, normalized size = 1.04 \begin {gather*} -50 \, x^{5} - \frac {325}{4} \, x^{4} - 15 \, x^{3} + \frac {81}{2} \, x^{2} + 27 \, x \end {gather*}

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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mupad [B]  time = 0.02, size = 24, normalized size = 1.04 \begin {gather*} -50\,x^5-\frac {325\,x^4}{4}-15\,x^3+\frac {81\,x^2}{2}+27\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)*(5*x + 3)^3,x)

[Out]

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

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sympy [A]  time = 0.06, size = 26, normalized size = 1.13 \begin {gather*} - 50 x^{5} - \frac {325 x^{4}}{4} - 15 x^{3} + \frac {81 x^{2}}{2} + 27 x \end {gather*}

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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