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

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

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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} $$\begin{array}{c}{e}^{289x^4}-3x^2\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =-3x^2+1156\int e^{289x^4}{x}^{3}dx\\ & =e^{289x^4}-3x^2\end{array}\end{array}$$

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

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)

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

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)

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

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)

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maple [A]  time = 0.02, size = 13, normalized size = 1.00

method	result	size
default	${\mathrm{e}}^{289x^4}-3x^2$	$13$
norman	${\mathrm{e}}^{289x^4}-3x^2$	$13$
risch	${\mathrm{e}}^{289x^4}-3x^2$	$13$

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

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

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)

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

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

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

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)

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