3.89.25 $\int \frac{e^{1-e^4+e^{e^4}+x^2}(-1+2x^2)}{x^2}dx$

Optimal. Leaf size=21 $$\frac{e^{1-e^4+e^{e^4}+x^2}}{x}$$

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Rubi [A]  time = 0.07, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 28, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.036, Rules used = {2288} $$\begin{array}{c}\frac{e^{x^2+e^{e^4}-e^4+1}}{x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(E^(1 - E^4 + E^E^4 + x^2)*(-1 + 2*x^2))/x^2,x]

[Out]

E^(1 - E^4 + E^E^4 + x^2)/x

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{e^{1-e^4+e^{e^4}+x^2}}{x}\end{array}\end{array}$$

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Mathematica [A]  time = 0.01, size = 21, normalized size = 1.00 $$\begin{array}{c}\frac{e^{1-e^4+e^{e^4}+x^2}}{x}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^(1 - E^4 + E^E^4 + x^2)*(-1 + 2*x^2))/x^2,x]

[Out]

E^(1 - E^4 + E^E^4 + x^2)/x

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fricas [A]  time = 0.51, size = 17, normalized size = 0.81 $$\begin{array}{c}{e}^{(x^2-e^4+e^{\left(e^4\right)}-\log (x)+1)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-1)*exp(-log(x)+exp(exp(4))-exp(4)+x^2+1)/x,x, algorithm="fricas")

[Out]

e^(x^2 - e^4 + e^(e^4) - log(x) + 1)

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giac [A]  time = 0.13, size = 17, normalized size = 0.81 $$\begin{array}{c}\frac{e^{(x^2-e^4+e^{\left(e^4\right)}+1)}}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-1)*exp(-log(x)+exp(exp(4))-exp(4)+x^2+1)/x,x, algorithm="giac")

[Out]

e^(x^2 - e^4 + e^(e^4) + 1)/x

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maple [A]  time = 0.03, size = 18, normalized size = 0.86

method	result	size
gosper	${\mathrm{e}}^{-\ln (x)+{\mathrm{e}}^{{\mathrm{e}}^4}-{\mathrm{e}}^4+x^2+1}$	$18$
norman	${\mathrm{e}}^{-\ln (x)+{\mathrm{e}}^{{\mathrm{e}}^4}-{\mathrm{e}}^4+x^2+1}$	$18$
risch	$\frac{{\mathrm{e}}^{1+{\mathrm{e}}^{{\mathrm{e}}^4}-{\mathrm{e}}^4+x^2}}{x}$	$18$
default	$\mathrm{e}{\mathrm{e}}^{{\mathrm{e}}^{{\mathrm{e}}^4}}{\mathrm{e}}^{-{\mathrm{e}}^4}\sqrt{\pi }\mathrm{erfi}(x)-\mathrm{e}{\mathrm{e}}^{{\mathrm{e}}^{{\mathrm{e}}^4}}{\mathrm{e}}^{-{\mathrm{e}}^4}(-\frac{{\mathrm{e}}^{x^2}}{x}+\sqrt{\pi }\mathrm{erfi}(x))$	$48$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2-1)*exp(-ln(x)+exp(exp(4))-exp(4)+x^2+1)/x,x,method=_RETURNVERBOSE)

[Out]

exp(-ln(x)+exp(exp(4))-exp(4)+x^2+1)

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maxima [C]  time = 0.41, size = 49, normalized size = 2.33 $$\begin{array}{c}-i\sqrt{\pi }\mathrm{erf}\left(ix\right)e^{(-e^4+e^{\left(e^4\right)}+1)}+\frac{\sqrt{-x^2}{e}^{(-e^4+e^{\left(e^4\right)}+1)}\mathrm{\Gamma }(-\frac{1}{2},-x^2)}{2x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-1)*exp(-log(x)+exp(exp(4))-exp(4)+x^2+1)/x,x, algorithm="maxima")

[Out]

-I*sqrt(pi)*erf(I*x)*e^(-e^4 + e^(e^4) + 1) + 1/2*sqrt(-x^2)*e^(-e^4 + e^(e^4) + 1)*gamma(-1/2, -x^2)/x

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mupad [B]  time = 5.36, size = 19, normalized size = 0.90 $$\begin{array}{c}\frac{{\mathrm{e}}^{-{\mathrm{e}}^4}{\mathrm{e}}^{{\mathrm{e}}^{{\mathrm{e}}^4}}{\mathrm{e}}^{x^2}\mathrm{e}}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(exp(4)) - exp(4) - log(x) + x^2 + 1)*(2*x^2 - 1))/x,x)

[Out]

(exp(-exp(4))*exp(exp(exp(4)))*exp(x^2)*exp(1))/x

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sympy [A]  time = 0.10, size = 15, normalized size = 0.71 $$\begin{array}{c}\frac{e^{x^2-e^4+1+e^{e^4}}}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x**2-1)*exp(-ln(x)+exp(exp(4))-exp(4)+x**2+1)/x,x)

[Out]

exp(x**2 - exp(4) + 1 + exp(exp(4)))/x

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