3.45.71 \(\int (-1+e^{x-x^4 \log (x)} (-24-4 x+7 x^2-x^3+24 x^4-10 x^5+x^6+(96 x^4-40 x^5+4 x^6) \log (x))) \, dx\)

Optimal. Leaf size=25 \[ \left (-1+e^{x-x^4 \log (x)} \left (1-(-5+x)^2\right )\right ) x \]

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Rubi [F]  time = 2.64, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \left (-1+e^{x-x^4 \log (x)} \left (-24-4 x+7 x^2-x^3+24 x^4-10 x^5+x^6+\left (96 x^4-40 x^5+4 x^6\right ) \log (x)\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[-1 + E^(x - x^4*Log[x])*(-24 - 4*x + 7*x^2 - x^3 + 24*x^4 - 10*x^5 + x^6 + (96*x^4 - 40*x^5 + 4*x^6)*Log[x
]),x]

[Out]

-x - 24*Defer[Int][E^(x - x^4*Log[x]), x] - 4*Defer[Int][E^(x - x^4*Log[x])*x, x] + 7*Defer[Int][E^(x - x^4*Lo
g[x])*x^2, x] - Defer[Int][E^(x - x^4*Log[x])*x^3, x] + 24*Defer[Int][E^(x - x^4*Log[x])*x^4, x] - 10*Defer[In
t][E^(x - x^4*Log[x])*x^5, x] + Defer[Int][E^(x - x^4*Log[x])*x^6, x] + 96*Defer[Int][E^(x - x^4*Log[x])*x^4*L
og[x], x] - 40*Defer[Int][E^(x - x^4*Log[x])*x^5*Log[x], x] + 4*Defer[Int][E^(x - x^4*Log[x])*x^6*Log[x], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^{x-x^4 \log (x)} \left (-24-4 x+7 x^2-x^3+24 x^4-10 x^5+x^6+\left (96 x^4-40 x^5+4 x^6\right ) \log (x)\right ) \, dx\\ &=-x+\int \left (-24 e^{x-x^4 \log (x)}-4 e^{x-x^4 \log (x)} x+7 e^{x-x^4 \log (x)} x^2-e^{x-x^4 \log (x)} x^3+24 e^{x-x^4 \log (x)} x^4-10 e^{x-x^4 \log (x)} x^5+e^{x-x^4 \log (x)} x^6+4 e^{x-x^4 \log (x)} x^4 \left (24-10 x+x^2\right ) \log (x)\right ) \, dx\\ &=-x-4 \int e^{x-x^4 \log (x)} x \, dx+4 \int e^{x-x^4 \log (x)} x^4 \left (24-10 x+x^2\right ) \log (x) \, dx+7 \int e^{x-x^4 \log (x)} x^2 \, dx-10 \int e^{x-x^4 \log (x)} x^5 \, dx-24 \int e^{x-x^4 \log (x)} \, dx+24 \int e^{x-x^4 \log (x)} x^4 \, dx-\int e^{x-x^4 \log (x)} x^3 \, dx+\int e^{x-x^4 \log (x)} x^6 \, dx\\ &=-x-4 \int e^{x-x^4 \log (x)} x \, dx+4 \int \left (24 e^{x-x^4 \log (x)} x^4 \log (x)-10 e^{x-x^4 \log (x)} x^5 \log (x)+e^{x-x^4 \log (x)} x^6 \log (x)\right ) \, dx+7 \int e^{x-x^4 \log (x)} x^2 \, dx-10 \int e^{x-x^4 \log (x)} x^5 \, dx-24 \int e^{x-x^4 \log (x)} \, dx+24 \int e^{x-x^4 \log (x)} x^4 \, dx-\int e^{x-x^4 \log (x)} x^3 \, dx+\int e^{x-x^4 \log (x)} x^6 \, dx\\ &=-x-4 \int e^{x-x^4 \log (x)} x \, dx+4 \int e^{x-x^4 \log (x)} x^6 \log (x) \, dx+7 \int e^{x-x^4 \log (x)} x^2 \, dx-10 \int e^{x-x^4 \log (x)} x^5 \, dx-24 \int e^{x-x^4 \log (x)} \, dx+24 \int e^{x-x^4 \log (x)} x^4 \, dx-40 \int e^{x-x^4 \log (x)} x^5 \log (x) \, dx+96 \int e^{x-x^4 \log (x)} x^4 \log (x) \, dx-\int e^{x-x^4 \log (x)} x^3 \, dx+\int e^{x-x^4 \log (x)} x^6 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 2.28, size = 26, normalized size = 1.04 \begin {gather*} -x-e^x x^{1-x^4} \left (24-10 x+x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + E^(x - x^4*Log[x])*(-24 - 4*x + 7*x^2 - x^3 + 24*x^4 - 10*x^5 + x^6 + (96*x^4 - 40*x^5 + 4*x^6)
*Log[x]),x]

[Out]

-x - E^x*x^(1 - x^4)*(24 - 10*x + x^2)

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fricas [A]  time = 0.61, size = 28, normalized size = 1.12 \begin {gather*} -{\left (x^{3} - 10 \, x^{2} + 24 \, x\right )} e^{\left (-x^{4} \log \relax (x) + x\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-40*x^5+96*x^4)*log(x)+x^6-10*x^5+24*x^4-x^3+7*x^2-4*x-24)*exp(-x^4*log(x)+x)-1,x, algorithm=
"fricas")

[Out]

-(x^3 - 10*x^2 + 24*x)*e^(-x^4*log(x) + x) - x

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (x^{6} - 10 \, x^{5} + 24 \, x^{4} - x^{3} + 7 \, x^{2} + 4 \, {\left (x^{6} - 10 \, x^{5} + 24 \, x^{4}\right )} \log \relax (x) - 4 \, x - 24\right )} e^{\left (-x^{4} \log \relax (x) + x\right )} - 1\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-40*x^5+96*x^4)*log(x)+x^6-10*x^5+24*x^4-x^3+7*x^2-4*x-24)*exp(-x^4*log(x)+x)-1,x, algorithm=
"giac")

[Out]

integrate((x^6 - 10*x^5 + 24*x^4 - x^3 + 7*x^2 + 4*(x^6 - 10*x^5 + 24*x^4)*log(x) - 4*x - 24)*e^(-x^4*log(x) +
x) - 1, x)

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maple [A]  time = 0.04, size = 25, normalized size = 1.00

method	result	size
risch	\(-x \left (x^{2}-10 x +24\right ) x^{-x^{4}} {\mathrm e}^{x}-x\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^6-40*x^5+96*x^4)*ln(x)+x^6-10*x^5+24*x^4-x^3+7*x^2-4*x-24)*exp(-x^4*ln(x)+x)-1,x,method=_RETURNVERBO
SE)

[Out]

-x*(x^2-10*x+24)*x^(-x^4)*exp(x)-x

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maxima [A]  time = 0.40, size = 28, normalized size = 1.12 \begin {gather*} -{\left (x^{3} - 10 \, x^{2} + 24 \, x\right )} e^{\left (-x^{4} \log \relax (x) + x\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-40*x^5+96*x^4)*log(x)+x^6-10*x^5+24*x^4-x^3+7*x^2-4*x-24)*exp(-x^4*log(x)+x)-1,x, algorithm=
"maxima")

[Out]

-(x^3 - 10*x^2 + 24*x)*e^(-x^4*log(x) + x) - x

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mupad [B]  time = 3.12, size = 27, normalized size = 1.08 \begin {gather*} -x-\frac {{\mathrm {e}}^x\,\left (x^3-10\,x^2+24\,x\right )}{x^{x^4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- exp(x - x^4*log(x))*(4*x - log(x)*(96*x^4 - 40*x^5 + 4*x^6) - 7*x^2 + x^3 - 24*x^4 + 10*x^5 - x^6 + 24)
- 1,x)

[Out]

- x - (exp(x)*(24*x - 10*x^2 + x^3))/x^(x^4)

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sympy [A]  time = 0.34, size = 22, normalized size = 0.88 \begin {gather*} - x + \left (- x^{3} + 10 x^{2} - 24 x\right ) e^{- x^{4} \log {\relax (x )} + x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**6-40*x**5+96*x**4)*ln(x)+x**6-10*x**5+24*x**4-x**3+7*x**2-4*x-24)*exp(-x**4*ln(x)+x)-1,x)

[Out]

-x + (-x**3 + 10*x**2 - 24*x)*exp(-x**4*log(x) + x)

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