3.82.20 \(\int \frac {1}{625} (625-12 e^{\frac {2 x^6}{625}} x^5) \, dx\)

Optimal. Leaf size=13 \[ -e^{\frac {2 x^6}{625}}+x \]

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Rubi [A]  time = 0.02, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2209} \begin {gather*} x-e^{\frac {2 x^6}{625}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(625 - 12*E^((2*x^6)/625)*x^5)/625,x]

[Out]

-E^((2*x^6)/625) + x

Rule 12

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

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{625} \int \left (625-12 e^{\frac {2 x^6}{625}} x^5\right ) \, dx\\ &=x-\frac {12}{625} \int e^{\frac {2 x^6}{625}} x^5 \, dx\\ &=-e^{\frac {2 x^6}{625}}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} -e^{\frac {2 x^6}{625}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(625 - 12*E^((2*x^6)/625)*x^5)/625,x]

[Out]

-E^((2*x^6)/625) + x

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fricas [A]  time = 0.50, size = 10, normalized size = 0.77 \begin {gather*} x - e^{\left (\frac {2}{625} \, x^{6}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/625*x^5*exp(2/625*x^6)+1,x, algorithm="fricas")

[Out]

x - e^(2/625*x^6)

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giac [A]  time = 0.21, size = 10, normalized size = 0.77 \begin {gather*} x - e^{\left (\frac {2}{625} \, x^{6}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/625*x^5*exp(2/625*x^6)+1,x, algorithm="giac")

[Out]

x - e^(2/625*x^6)

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maple [A]  time = 0.02, size = 11, normalized size = 0.85

method	result	size
default	\(x -{\mathrm e}^{\frac {2 x^{6}}{625}}\)	\(11\)
norman	\(x -{\mathrm e}^{\frac {2 x^{6}}{625}}\)	\(11\)
risch	\(x -{\mathrm e}^{\frac {2 x^{6}}{625}}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-12/625*x^5*exp(2/625*x^6)+1,x,method=_RETURNVERBOSE)

[Out]

x-exp(2/625*x^6)

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maxima [A]  time = 0.37, size = 10, normalized size = 0.77 \begin {gather*} x - e^{\left (\frac {2}{625} \, x^{6}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/625*x^5*exp(2/625*x^6)+1,x, algorithm="maxima")

[Out]

x - e^(2/625*x^6)

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mupad [B]  time = 5.78, size = 10, normalized size = 0.77 \begin {gather*} x-{\mathrm {e}}^{\frac {2\,x^6}{625}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - (12*x^5*exp((2*x^6)/625))/625,x)

[Out]

x - exp((2*x^6)/625)

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sympy [A]  time = 0.09, size = 8, normalized size = 0.62 \begin {gather*} x - e^{\frac {2 x^{6}}{625}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/625*x**5*exp(2/625*x**6)+1,x)

[Out]

x - exp(2*x**6/625)

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