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

Optimal. Leaf size=13 \[ e^{289 x^4}-3 x^2 \]

________________________________________________________________________________________

Rubi [A]  time = 0.03, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2209} \begin {gather*} e^{289 x^4}-3 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-6*x + 1156*E^(289*x^4)*x^3,x]

[Out]

E^(289*x^4) - 3*x^2

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

________________________________________________________________________________________

Mathematica [A]  time = 0.01, size = 21, normalized size = 1.62 \begin {gather*} 2 \left (\frac {e^{289 x^4}}{2}-\frac {3 x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

2*(E^(289*x^4)/2 - (3*x^2)/2)

________________________________________________________________________________________

fricas [A]  time = 0.75, size = 12, normalized size = 0.92 \begin {gather*} -3 \, x^{2} + e^{\left (289 \, x^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x^2 + e^(289*x^4)

________________________________________________________________________________________

giac [A]  time = 0.17, size = 12, normalized size = 0.92 \begin {gather*} -3 \, x^{2} + e^{\left (289 \, x^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x^2 + e^(289*x^4)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 13, normalized size = 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	\({\mathrm e}^{289 x^{4}}-3 x^{2}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.34, size = 12, normalized size = 0.92 \begin {gather*} -3 \, x^{2} + e^{\left (289 \, x^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x^2 + e^(289*x^4)

________________________________________________________________________________________

mupad [B]  time = 0.05, size = 12, normalized size = 0.92 \begin {gather*} {\mathrm {e}}^{289\,x^4}-3\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1156*x^3*exp(289*x^4) - 6*x,x)

[Out]

exp(289*x^4) - 3*x^2

________________________________________________________________________________________

sympy [A]  time = 0.09, size = 10, normalized size = 0.77 \begin {gather*} - 3 x^{2} + e^{289 x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3*x**2 + exp(289*x**4)

________________________________________________________________________________________