3.1346 \(\int (1-2 x)^3 (3+5 x) \, dx\)

Optimal. Leaf size=23 \[ \frac {1}{4} (1-2 x)^5-\frac {11}{16} (1-2 x)^4 \]

[Out]

-11/16*(1-2*x)^4+1/4*(1-2*x)^5

________________________________________________________________________________________

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} \[ \frac {1}{4} (1-2 x)^5-\frac {11}{16} (1-2 x)^4 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(3 + 5*x),x]

[Out]

(-11*(1 - 2*x)^4)/16 + (1 - 2*x)^5/4

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 (3+5 x) \, dx &=\int \left (\frac {11}{2} (1-2 x)^3-\frac {5}{2} (1-2 x)^4\right ) \, dx\\ &=-\frac {11}{16} (1-2 x)^4+\frac {1}{4} (1-2 x)^5\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 26, normalized size = 1.13 \[ -8 x^5+9 x^4+2 x^3-\frac {13 x^2}{2}+3 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(3 + 5*x),x]

[Out]

3*x - (13*x^2)/2 + 2*x^3 + 9*x^4 - 8*x^5

________________________________________________________________________________________

fricas [A]  time = 0.68, size = 24, normalized size = 1.04 \[ -8 x^{5} + 9 x^{4} + 2 x^{3} - \frac {13}{2} x^{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x

________________________________________________________________________________________

giac [A]  time = 0.90, size = 24, normalized size = 1.04 \[ -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac {13}{2} \, x^{2} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x

________________________________________________________________________________________

maple [A]  time = 0.00, size = 25, normalized size = 1.09 \[ -8 x^{5}+9 x^{4}+2 x^{3}-\frac {13}{2} x^{2}+3 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x^5+9*x^4+2*x^3-13/2*x^2+3*x

________________________________________________________________________________________

maxima [A]  time = 0.59, size = 24, normalized size = 1.04 \[ -8 \, x^{5} + 9 \, x^{4} + 2 \, x^{3} - \frac {13}{2} \, x^{2} + 3 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x

________________________________________________________________________________________

mupad [B]  time = 0.02, size = 24, normalized size = 1.04 \[ -8\,x^5+9\,x^4+2\,x^3-\frac {13\,x^2}{2}+3\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)^3*(5*x + 3),x)

[Out]

3*x - (13*x^2)/2 + 2*x^3 + 9*x^4 - 8*x^5

________________________________________________________________________________________

sympy [A]  time = 0.06, size = 24, normalized size = 1.04 \[ - 8 x^{5} + 9 x^{4} + 2 x^{3} - \frac {13 x^{2}}{2} + 3 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x**5 + 9*x**4 + 2*x**3 - 13*x**2/2 + 3*x

________________________________________________________________________________________