\(\int (-1+5000 e^{625 x^8} x^7) \, dx\) [399]

Optimal result

Integrand size = 14, antiderivative size = 11 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=e^{625 x^8}-x \]

[Out]

-x+exp(625*x^8)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2240} \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=e^{625 x^8}-x \]

[In]

Int[-1 + 5000*E^(625*x^8)*x^7,x]

[Out]

E^(625*x^8) - x

Rule 2240

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{align*} \text {integral}& = -x+5000 \int e^{625 x^8} x^7 \, dx \\ & = e^{625 x^8}-x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=e^{625 x^8}-x \]

[In]

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

[Out]

E^(625*x^8) - x

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

-x+exp(625*x^8)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=-x + e^{\left (625 \, x^{8}\right )} \]

[In]

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

[Out]

-x + e^(625*x^8)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=- x + e^{625 x^{8}} \]

[In]

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

[Out]

-x + exp(625*x**8)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=-x + e^{\left (625 \, x^{8}\right )} \]

[In]

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

[Out]

-x + e^(625*x^8)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=-x + e^{\left (625 \, x^{8}\right )} \]

[In]

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

[Out]

-x + e^(625*x^8)

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx={\mathrm {e}}^{625\,x^8}-x \]

[In]

int(5000*x^7*exp(625*x^8) - 1,x)

[Out]

exp(625*x^8) - x