3.86.25 \(\int \frac {1}{5} (7+e^3+14 x-15 x^2) \, dx\)

Optimal. Leaf size=32 \[ x \left (2-x \left (-1+x+\frac {1}{5} \left (\frac {3}{x}-\frac {e^3+2 x}{x}\right )\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 23, normalized size of antiderivative = 0.72, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {12} \begin {gather*} -x^3+\frac {7 x^2}{5}+\frac {1}{5} \left (7+e^3\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(7 + E^3 + 14*x - 15*x^2)/5,x]

[Out]

((7 + E^3)*x)/5 + (7*x^2)/5 - x^3

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (7+e^3+14 x-15 x^2\right ) \, dx\\ &=\frac {1}{5} \left (7+e^3\right ) x+\frac {7 x^2}{5}-x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 23, normalized size = 0.72 \begin {gather*} \frac {1}{5} \left (7 x+e^3 x+7 x^2-5 x^3\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(7 + E^3 + 14*x - 15*x^2)/5,x]

[Out]

(7*x + E^3*x + 7*x^2 - 5*x^3)/5

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fricas [A]  time = 0.70, size = 19, normalized size = 0.59 \begin {gather*} -x^{3} + \frac {7}{5} \, x^{2} + \frac {1}{5} \, x e^{3} + \frac {7}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*exp(3)-3*x^2+14/5*x+7/5,x, algorithm="fricas")

[Out]

-x^3 + 7/5*x^2 + 1/5*x*e^3 + 7/5*x

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giac [A]  time = 0.14, size = 19, normalized size = 0.59 \begin {gather*} -x^{3} + \frac {7}{5} \, x^{2} + \frac {1}{5} \, x e^{3} + \frac {7}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*exp(3)-3*x^2+14/5*x+7/5,x, algorithm="giac")

[Out]

-x^3 + 7/5*x^2 + 1/5*x*e^3 + 7/5*x

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maple [A]  time = 0.03, size = 16, normalized size = 0.50

method	result	size
gosper	\(\frac {x \left (-5 x^{2}+{\mathrm e}^{3}+7 x +7\right )}{5}\)	\(16\)
default	\(\frac {x \,{\mathrm e}^{3}}{5}-x^{3}+\frac {7 x^{2}}{5}+\frac {7 x}{5}\)	\(20\)
norman	\(\left (\frac {7}{5}+\frac {{\mathrm e}^{3}}{5}\right ) x +\frac {7 x^{2}}{5}-x^{3}\)	\(20\)
risch	\(\frac {x \,{\mathrm e}^{3}}{5}-x^{3}+\frac {7 x^{2}}{5}+\frac {7 x}{5}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/5*exp(3)-3*x^2+14/5*x+7/5,x,method=_RETURNVERBOSE)

[Out]

1/5*x*(-5*x^2+exp(3)+7*x+7)

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maxima [A]  time = 0.36, size = 19, normalized size = 0.59 \begin {gather*} -x^{3} + \frac {7}{5} \, x^{2} + \frac {1}{5} \, x e^{3} + \frac {7}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*exp(3)-3*x^2+14/5*x+7/5,x, algorithm="maxima")

[Out]

-x^3 + 7/5*x^2 + 1/5*x*e^3 + 7/5*x

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mupad [B]  time = 0.03, size = 15, normalized size = 0.47 \begin {gather*} \frac {x\,\left (-5\,x^2+7\,x+{\mathrm {e}}^3+7\right )}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((14*x)/5 + exp(3)/5 - 3*x^2 + 7/5,x)

[Out]

(x*(7*x + exp(3) - 5*x^2 + 7))/5

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sympy [A]  time = 0.06, size = 19, normalized size = 0.59 \begin {gather*} - x^{3} + \frac {7 x^{2}}{5} + x \left (\frac {7}{5} + \frac {e^{3}}{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*exp(3)-3*x**2+14/5*x+7/5,x)

[Out]

-x**3 + 7*x**2/5 + x*(7/5 + exp(3)/5)

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