3.1166 \(\int (1-2 x) (3+5 x)^2 \, dx\)

Optimal. Leaf size=23 \[ -\frac {25 x^4}{2}-\frac {35 x^3}{3}+6 x^2+9 x \]

[Out]

9*x+6*x^2-35/3*x^3-25/2*x^4

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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} \[ -\frac {25 x^4}{2}-\frac {35 x^3}{3}+6 x^2+9 x \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)*(3 + 5*x)^2,x]

[Out]

9*x + 6*x^2 - (35*x^3)/3 - (25*x^4)/2

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)^2 \, dx &=\int \left (9+12 x-35 x^2-50 x^3\right ) \, dx\\ &=9 x+6 x^2-\frac {35 x^3}{3}-\frac {25 x^4}{2}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 23, normalized size = 1.00 \[ -\frac {25 x^4}{2}-\frac {35 x^3}{3}+6 x^2+9 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)*(3 + 5*x)^2,x]

[Out]

9*x + 6*x^2 - (35*x^3)/3 - (25*x^4)/2

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fricas [A]  time = 0.57, size = 19, normalized size = 0.83 \[ -\frac {25}{2} x^{4} - \frac {35}{3} x^{3} + 6 x^{2} + 9 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25/2*x^4 - 35/3*x^3 + 6*x^2 + 9*x

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giac [A]  time = 1.15, size = 19, normalized size = 0.83 \[ -\frac {25}{2} \, x^{4} - \frac {35}{3} \, x^{3} + 6 \, x^{2} + 9 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25/2*x^4 - 35/3*x^3 + 6*x^2 + 9*x

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maple [A]  time = 0.00, size = 20, normalized size = 0.87 \[ -\frac {25}{2} x^{4}-\frac {35}{3} x^{3}+6 x^{2}+9 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

9*x+6*x^2-35/3*x^3-25/2*x^4

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maxima [A]  time = 0.49, size = 19, normalized size = 0.83 \[ -\frac {25}{2} \, x^{4} - \frac {35}{3} \, x^{3} + 6 \, x^{2} + 9 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25/2*x^4 - 35/3*x^3 + 6*x^2 + 9*x

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mupad [B]  time = 0.03, size = 19, normalized size = 0.83 \[ -\frac {25\,x^4}{2}-\frac {35\,x^3}{3}+6\,x^2+9\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)*(5*x + 3)^2,x)

[Out]

9*x + 6*x^2 - (35*x^3)/3 - (25*x^4)/2

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sympy [A]  time = 0.06, size = 20, normalized size = 0.87 \[ - \frac {25 x^{4}}{2} - \frac {35 x^{3}}{3} + 6 x^{2} + 9 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-25*x**4/2 - 35*x**3/3 + 6*x**2 + 9*x

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