3.4.99 \(\int (-1+5000 e^{625 x^8} x^7) \, dx\)

Optimal. Leaf size=11 \[ e^{625 x^8}-x \]

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Rubi [A]  time = 0.02, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2209} \begin {gather*} e^{625 x^8}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + 5000*E^(625*x^8)*x^7,x]

[Out]

E^(625*x^8) - 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} &=-x+5000 \int e^{625 x^8} x^7 \, dx\\ &=e^{625 x^8}-x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} e^{625 x^8}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + 5000*E^(625*x^8)*x^7,x]

[Out]

E^(625*x^8) - x

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fricas [A]  time = 0.56, size = 10, normalized size = 0.91 \begin {gather*} -x + e^{\left (625 \, x^{8}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5000*x^7*exp(625*x^8)-1,x, algorithm="fricas")

[Out]

-x + e^(625*x^8)

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giac [A]  time = 0.33, size = 10, normalized size = 0.91 \begin {gather*} -x + e^{\left (625 \, x^{8}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5000*x^7*exp(625*x^8)-1,x, algorithm="giac")

[Out]

-x + e^(625*x^8)

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maple [A]  time = 0.02, size = 11, normalized size = 1.00

method	result	size
default	\(-x +{\mathrm e}^{625 x^{8}}\)	\(11\)
norman	\(-x +{\mathrm e}^{625 x^{8}}\)	\(11\)
risch	\(-x +{\mathrm e}^{625 x^{8}}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5000*x^7*exp(625*x^8)-1,x,method=_RETURNVERBOSE)

[Out]

-x+exp(625*x^8)

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maxima [A]  time = 0.42, size = 10, normalized size = 0.91 \begin {gather*} -x + e^{\left (625 \, x^{8}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5000*x^7*exp(625*x^8)-1,x, algorithm="maxima")

[Out]

-x + e^(625*x^8)

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mupad [B]  time = 0.44, size = 10, normalized size = 0.91 \begin {gather*} {\mathrm {e}}^{625\,x^8}-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5000*x^7*exp(625*x^8) - 1,x)

[Out]

exp(625*x^8) - x

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sympy [A]  time = 0.09, size = 7, normalized size = 0.64 \begin {gather*} - x + e^{625 x^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5000*x**7*exp(625*x**8)-1,x)

[Out]

-x + exp(625*x**8)

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