3.43.87 \(\int ((-88 e^5+88 e^{4 x}) \log (x)+(-44 e^5+e^{4 x} (44+176 x)) \log ^2(x)) \, dx\)

Optimal. Leaf size=18 \[ -44 \left (e^5-e^{4 x}\right ) x \log ^2(x) \]

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Rubi [F]  time = 0.23, 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 (\left (-88 e^5+88 e^{4 x}\right ) \log (x)+\left (-44 e^5+e^{4 x} (44+176 x)\right ) \log ^2(x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-88*E^5 + 88*E^(4*x))*Log[x] + (-44*E^5 + E^(4*x)*(44 + 176*x))*Log[x]^2,x]

[Out]

-22*ExpIntegralEi[4*x] + 22*E^(4*x)*Log[x] - 44*E^5*x*Log[x]^2 + 44*Defer[Int][E^(4*x)*Log[x]^2, x] + 176*Defe
r[Int][E^(4*x)*x*Log[x]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-88 e^5+88 e^{4 x}\right ) \log (x) \, dx+\int \left (-44 e^5+e^{4 x} (44+176 x)\right ) \log ^2(x) \, dx\\ &=22 e^{4 x} \log (x)-88 e^5 x \log (x)-\int \frac {22 \left (e^{4 x}-4 e^5 x\right )}{x} \, dx+\int \left (-44 e^5 \log ^2(x)+44 e^{4 x} (1+4 x) \log ^2(x)\right ) \, dx\\ &=22 e^{4 x} \log (x)-88 e^5 x \log (x)-22 \int \frac {e^{4 x}-4 e^5 x}{x} \, dx+44 \int e^{4 x} (1+4 x) \log ^2(x) \, dx-\left (44 e^5\right ) \int \log ^2(x) \, dx\\ &=22 e^{4 x} \log (x)-88 e^5 x \log (x)-44 e^5 x \log ^2(x)-22 \int \left (-4 e^5+\frac {e^{4 x}}{x}\right ) \, dx+44 \int \left (e^{4 x} \log ^2(x)+4 e^{4 x} x \log ^2(x)\right ) \, dx+\left (88 e^5\right ) \int \log (x) \, dx\\ &=22 e^{4 x} \log (x)-44 e^5 x \log ^2(x)-22 \int \frac {e^{4 x}}{x} \, dx+44 \int e^{4 x} \log ^2(x) \, dx+176 \int e^{4 x} x \log ^2(x) \, dx\\ &=-22 \text {Ei}(4 x)+22 e^{4 x} \log (x)-44 e^5 x \log ^2(x)+44 \int e^{4 x} \log ^2(x) \, dx+176 \int e^{4 x} x \log ^2(x) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 18, normalized size = 1.00 \begin {gather*} 44 \left (-e^5+e^{4 x}\right ) x \log ^2(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-88*E^5 + 88*E^(4*x))*Log[x] + (-44*E^5 + E^(4*x)*(44 + 176*x))*Log[x]^2,x]

[Out]

44*(-E^5 + E^(4*x))*x*Log[x]^2

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fricas [A]  time = 0.54, size = 18, normalized size = 1.00 \begin {gather*} -44 \, {\left (x e^{5} - x e^{\left (4 \, x\right )}\right )} \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((176*x+44)*exp(4*x)-44*exp(5))*log(x)^2+(88*exp(4*x)-88*exp(5))*log(x),x, algorithm="fricas")

[Out]

-44*(x*e^5 - x*e^(4*x))*log(x)^2

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giac [B]  time = 0.20, size = 60, normalized size = 3.33 \begin {gather*} -44 \, {\left (x e^{5} - x e^{\left (4 \, x\right )}\right )} \log \relax (x)^{2} + 88 \, {\left (x \log \relax (x) - x\right )} e^{5} + 88 \, x e^{5} - 22 \, {\left (4 \, x e^{5} - e^{\left (4 \, x\right )}\right )} \log \relax (x) - 22 \, e^{\left (4 \, x\right )} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((176*x+44)*exp(4*x)-44*exp(5))*log(x)^2+(88*exp(4*x)-88*exp(5))*log(x),x, algorithm="giac")

[Out]

-44*(x*e^5 - x*e^(4*x))*log(x)^2 + 88*(x*log(x) - x)*e^5 + 88*x*e^5 - 22*(4*x*e^5 - e^(4*x))*log(x) - 22*e^(4*
x)*log(x)

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maple [A]  time = 0.10, size = 22, normalized size = 1.22

method	result	size
default	\(44 \,{\mathrm e}^{4 x} \ln \relax (x )^{2} x -44 x \,{\mathrm e}^{5} \ln \relax (x )^{2}\)	\(22\)
norman	\(44 \,{\mathrm e}^{4 x} \ln \relax (x )^{2} x -44 x \,{\mathrm e}^{5} \ln \relax (x )^{2}\)	\(22\)
risch	\(44 \,{\mathrm e}^{4 x} \ln \relax (x )^{2} x -44 x \,{\mathrm e}^{5} \ln \relax (x )^{2}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((176*x+44)*exp(4*x)-44*exp(5))*ln(x)^2+(88*exp(4*x)-88*exp(5))*ln(x),x,method=_RETURNVERBOSE)

[Out]

44*exp(4*x)*ln(x)^2*x-44*x*exp(5)*ln(x)^2

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maxima [A]  time = 0.38, size = 21, normalized size = 1.17 \begin {gather*} -44 \, x e^{5} \log \relax (x)^{2} + 44 \, x e^{\left (4 \, x\right )} \log \relax (x)^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((176*x+44)*exp(4*x)-44*exp(5))*log(x)^2+(88*exp(4*x)-88*exp(5))*log(x),x, algorithm="maxima")

[Out]

-44*x*e^5*log(x)^2 + 44*x*e^(4*x)*log(x)^2

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mupad [B]  time = 3.21, size = 16, normalized size = 0.89 \begin {gather*} 44\,x\,{\ln \relax (x)}^2\,\left ({\mathrm {e}}^{4\,x}-{\mathrm {e}}^5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(x)*(88*exp(4*x) - 88*exp(5)) - log(x)^2*(44*exp(5) - exp(4*x)*(176*x + 44)),x)

[Out]

44*x*log(x)^2*(exp(4*x) - exp(5))

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sympy [A]  time = 0.34, size = 24, normalized size = 1.33 \begin {gather*} 44 x e^{4 x} \log {\relax (x )}^{2} - 44 x e^{5} \log {\relax (x )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((176*x+44)*exp(4*x)-44*exp(5))*ln(x)**2+(88*exp(4*x)-88*exp(5))*ln(x),x)

[Out]

44*x*exp(4*x)*log(x)**2 - 44*x*exp(5)*log(x)**2

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