\(\int (-6 x+1156 e^{289 x^4} x^3) \, dx\) [3267]

Optimal result

Integrand size = 16, antiderivative size = 13 \[ \int \left (-6 x+1156 e^{289 x^4} x^3\right ) \, dx=e^{289 x^4}-3 x^2 \]

[Out]

exp(289*x^4)-3*x^2

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2240} \[ \int \left (-6 x+1156 e^{289 x^4} x^3\right ) \, dx=e^{289 x^4}-3 x^2 \]

[In]

Int[-6*x + 1156*E^(289*x^4)*x^3,x]

[Out]

E^(289*x^4) - 3*x^2

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}& = -3 x^2+1156 \int e^{289 x^4} x^3 \, dx \\ & = e^{289 x^4}-3 x^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.08 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (-6 x+1156 e^{289 x^4} x^3\right ) \, dx=e^{289 x^4}-3 x^2 \]

[In]

Integrate[-6*x + 1156*E^(289*x^4)*x^3,x]

[Out]

E^(289*x^4) - 3*x^2

Maple [A] (verified)

Time = 0.20 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00

method	result	size
default	\({\mathrm e}^{289 x^{4}}-3 x^{2}\)	\(13\)
norman	\({\mathrm e}^{289 x^{4}}-3 x^{2}\)	\(13\)
risch	\({\mathrm e}^{289 x^{4}}-3 x^{2}\)	\(13\)
parallelrisch	\({\mathrm e}^{289 x^{4}}-3 x^{2}\)	\(13\)
parts	\({\mathrm e}^{289 x^{4}}-3 x^{2}\)	\(13\)

[In]

int(1156*x^3*exp(289*x^4)-6*x,x,method=_RETURNVERBOSE)

[Out]

exp(289*x^4)-3*x^2

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \left (-6 x+1156 e^{289 x^4} x^3\right ) \, dx=-3 \, x^{2} + e^{\left (289 \, x^{4}\right )} \]

[In]

integrate(1156*x^3*exp(289*x^4)-6*x,x, algorithm="fricas")

[Out]

-3*x^2 + e^(289*x^4)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (-6 x+1156 e^{289 x^4} x^3\right ) \, dx=- 3 x^{2} + e^{289 x^{4}} \]

[In]

integrate(1156*x**3*exp(289*x**4)-6*x,x)

[Out]

-3*x**2 + exp(289*x**4)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \left (-6 x+1156 e^{289 x^4} x^3\right ) \, dx=-3 \, x^{2} + e^{\left (289 \, x^{4}\right )} \]

[In]

integrate(1156*x^3*exp(289*x^4)-6*x,x, algorithm="maxima")

[Out]

-3*x^2 + e^(289*x^4)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \left (-6 x+1156 e^{289 x^4} x^3\right ) \, dx=-3 \, x^{2} + e^{\left (289 \, x^{4}\right )} \]

[In]

integrate(1156*x^3*exp(289*x^4)-6*x,x, algorithm="giac")

[Out]

-3*x^2 + e^(289*x^4)

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \left (-6 x+1156 e^{289 x^4} x^3\right ) \, dx={\mathrm {e}}^{289\,x^4}-3\,x^2 \]

[In]

int(1156*x^3*exp(289*x^4) - 6*x,x)

[Out]

exp(289*x^4) - 3*x^2