3.100.96 \(\int \frac {1}{25} (25-15 e x^2-24 x^3) \, dx\)

Optimal. Leaf size=24 \[ x+x^2-x \left (x+\frac {1}{5} x^2 \left (e+\frac {6 x}{5}\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.71, 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*} -\frac {6 x^4}{25}-\frac {e x^3}{5}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(25 - 15*E*x^2 - 24*x^3)/25,x]

[Out]

x - (E*x^3)/5 - (6*x^4)/25

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}{25} \int \left (25-15 e x^2-24 x^3\right ) \, dx\\ &=x-\frac {e x^3}{5}-\frac {6 x^4}{25}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 0.71 \begin {gather*} x-\frac {e x^3}{5}-\frac {6 x^4}{25} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(25 - 15*E*x^2 - 24*x^3)/25,x]

[Out]

x - (E*x^3)/5 - (6*x^4)/25

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fricas [A]  time = 0.60, size = 14, normalized size = 0.58 \begin {gather*} -\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/5*x^2*exp(1)-24/25*x^3+1,x, algorithm="fricas")

[Out]

-6/25*x^4 - 1/5*x^3*e + x

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giac [A]  time = 0.14, size = 14, normalized size = 0.58 \begin {gather*} -\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/5*x^2*exp(1)-24/25*x^3+1,x, algorithm="giac")

[Out]

-6/25*x^4 - 1/5*x^3*e + x

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maple [A]  time = 0.02, size = 15, normalized size = 0.62

method	result	size
default	\(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\)	\(15\)
norman	\(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\)	\(15\)
risch	\(-\frac {x^{3} {\mathrm e}}{5}-\frac {6 x^{4}}{25}+x\)	\(15\)
gosper	\(-\frac {x \left (5 x^{2} {\mathrm e}+6 x^{3}-25\right )}{25}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3/5*x^2*exp(1)-24/25*x^3+1,x,method=_RETURNVERBOSE)

[Out]

-1/5*x^3*exp(1)-6/25*x^4+x

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maxima [A]  time = 0.35, size = 14, normalized size = 0.58 \begin {gather*} -\frac {6}{25} \, x^{4} - \frac {1}{5} \, x^{3} e + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/5*x^2*exp(1)-24/25*x^3+1,x, algorithm="maxima")

[Out]

-6/25*x^4 - 1/5*x^3*e + x

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mupad [B]  time = 0.04, size = 14, normalized size = 0.58 \begin {gather*} -\frac {6\,x^4}{25}-\frac {\mathrm {e}\,x^3}{5}+x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - (24*x^3)/25 - (3*x^2*exp(1))/5,x)

[Out]

x - (x^3*exp(1))/5 - (6*x^4)/25

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sympy [A]  time = 0.05, size = 15, normalized size = 0.62 \begin {gather*} - \frac {6 x^{4}}{25} - \frac {e x^{3}}{5} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/5*x**2*exp(1)-24/25*x**3+1,x)

[Out]

-6*x**4/25 - E*x**3/5 + x

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