3.62.13 \(\int (17-14 x+3 x^2+e^{-30 x+4 x^2+2 x^3} (1-30 x+8 x^2+6 x^3)+e^{-15 x+2 x^2+x^3} (8-124 x+62 x^2+16 x^3-6 x^4)+\log (\log (2))) \, dx\)

Optimal. Leaf size=25 \[ x \left (1+\left (4+e^{(-3+x) x (5+x)}-x\right )^2+x+\log (\log (2))\right ) \]

________________________________________________________________________________________

Rubi [F]  time = 0.33, 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 (17-14 x+3 x^2+e^{-30 x+4 x^2+2 x^3} \left (1-30 x+8 x^2+6 x^3\right )+e^{-15 x+2 x^2+x^3} \left (8-124 x+62 x^2+16 x^3-6 x^4\right )+\log (\log (2))\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[17 - 14*x + 3*x^2 + E^(-30*x + 4*x^2 + 2*x^3)*(1 - 30*x + 8*x^2 + 6*x^3) + E^(-15*x + 2*x^2 + x^3)*(8 - 12
4*x + 62*x^2 + 16*x^3 - 6*x^4) + Log[Log[2]],x]

[Out]

-7*x^2 + x^3 + (E^(-30*x + 4*x^2 + 2*x^3)*(15*x - 4*x^2 - 3*x^3))/(15 - 4*x - 3*x^2) + x*(17 + Log[Log[2]]) +
8*Defer[Int][E^(-15*x + 2*x^2 + x^3), x] - 124*Defer[Int][E^(-15*x + 2*x^2 + x^3)*x, x] + 62*Defer[Int][E^(-15
*x + 2*x^2 + x^3)*x^2, x] + 16*Defer[Int][E^(-15*x + 2*x^2 + x^3)*x^3, x] - 6*Defer[Int][E^(-15*x + 2*x^2 + x^
3)*x^4, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-7 x^2+x^3+x (17+\log (\log (2)))+\int e^{-30 x+4 x^2+2 x^3} \left (1-30 x+8 x^2+6 x^3\right ) \, dx+\int e^{-15 x+2 x^2+x^3} \left (8-124 x+62 x^2+16 x^3-6 x^4\right ) \, dx\\ &=-7 x^2+x^3+\frac {e^{-30 x+4 x^2+2 x^3} \left (15 x-4 x^2-3 x^3\right )}{15-4 x-3 x^2}+x (17+\log (\log (2)))+\int \left (8 e^{-15 x+2 x^2+x^3}-124 e^{-15 x+2 x^2+x^3} x+62 e^{-15 x+2 x^2+x^3} x^2+16 e^{-15 x+2 x^2+x^3} x^3-6 e^{-15 x+2 x^2+x^3} x^4\right ) \, dx\\ &=-7 x^2+x^3+\frac {e^{-30 x+4 x^2+2 x^3} \left (15 x-4 x^2-3 x^3\right )}{15-4 x-3 x^2}+x (17+\log (\log (2)))-6 \int e^{-15 x+2 x^2+x^3} x^4 \, dx+8 \int e^{-15 x+2 x^2+x^3} \, dx+16 \int e^{-15 x+2 x^2+x^3} x^3 \, dx+62 \int e^{-15 x+2 x^2+x^3} x^2 \, dx-124 \int e^{-15 x+2 x^2+x^3} x \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.20, size = 53, normalized size = 2.12 \begin {gather*} e^{-15 x} x \left (e^{x \left (-15+4 x+2 x^2\right )}-2 e^{x^2 (2+x)} (-4+x)+e^{15 x} \left (17-7 x+x^2+\log (\log (2))\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[17 - 14*x + 3*x^2 + E^(-30*x + 4*x^2 + 2*x^3)*(1 - 30*x + 8*x^2 + 6*x^3) + E^(-15*x + 2*x^2 + x^3)*(
8 - 124*x + 62*x^2 + 16*x^3 - 6*x^4) + Log[Log[2]],x]

[Out]

(x*(E^(x*(-15 + 4*x + 2*x^2)) - 2*E^(x^2*(2 + x))*(-4 + x) + E^(15*x)*(17 - 7*x + x^2 + Log[Log[2]])))/E^(15*x
)

________________________________________________________________________________________

fricas [B]  time = 0.72, size = 56, normalized size = 2.24 \begin {gather*} x^{3} - 7 \, x^{2} + x e^{\left (2 \, x^{3} + 4 \, x^{2} - 30 \, x\right )} - 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{3} + 2 \, x^{2} - 15 \, x\right )} + x \log \left (\log \relax (2)\right ) + 17 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(2))+(6*x^3+8*x^2-30*x+1)*exp(x^3+2*x^2-15*x)^2+(-6*x^4+16*x^3+62*x^2-124*x+8)*exp(x^3+2*x^2-
15*x)+3*x^2-14*x+17,x, algorithm="fricas")

[Out]

x^3 - 7*x^2 + x*e^(2*x^3 + 4*x^2 - 30*x) - 2*(x^2 - 4*x)*e^(x^3 + 2*x^2 - 15*x) + x*log(log(2)) + 17*x

________________________________________________________________________________________

giac [B]  time = 0.14, size = 68, normalized size = 2.72 \begin {gather*} x^{3} - 2 \, x^{2} e^{\left (x^{3} + 2 \, x^{2} - 15 \, x\right )} - 7 \, x^{2} + x e^{\left (2 \, x^{3} + 4 \, x^{2} - 30 \, x\right )} + 8 \, x e^{\left (x^{3} + 2 \, x^{2} - 15 \, x\right )} + x \log \left (\log \relax (2)\right ) + 17 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(2))+(6*x^3+8*x^2-30*x+1)*exp(x^3+2*x^2-15*x)^2+(-6*x^4+16*x^3+62*x^2-124*x+8)*exp(x^3+2*x^2-
15*x)+3*x^2-14*x+17,x, algorithm="giac")

[Out]

x^3 - 2*x^2*e^(x^3 + 2*x^2 - 15*x) - 7*x^2 + x*e^(2*x^3 + 4*x^2 - 30*x) + 8*x*e^(x^3 + 2*x^2 - 15*x) + x*log(l
og(2)) + 17*x

________________________________________________________________________________________

maple [A]  time = 0.09, size = 49, normalized size = 1.96

method	result	size
risch	\(x \ln \left (\ln \relax (2)\right )+{\mathrm e}^{2 \left (x -3\right ) \left (5+x \right ) x} x +\left (-2 x^{2}+8 x \right ) {\mathrm e}^{\left (x -3\right ) \left (5+x \right ) x}+x^{3}-7 x^{2}+17 x\)	\(49\)
norman	\(x^{3}+\left (\ln \left (\ln \relax (2)\right )+17\right ) x +{\mathrm e}^{2 x^{3}+4 x^{2}-30 x} x -7 x^{2}+8 \,{\mathrm e}^{x^{3}+2 x^{2}-15 x} x -2 \,{\mathrm e}^{x^{3}+2 x^{2}-15 x} x^{2}\)	\(68\)
default	\(17 x +{\mathrm e}^{2 x^{3}+4 x^{2}-30 x} x +8 \,{\mathrm e}^{x^{3}+2 x^{2}-15 x} x -2 \,{\mathrm e}^{x^{3}+2 x^{2}-15 x} x^{2}-7 x^{2}+x^{3}+x \ln \left (\ln \relax (2)\right )\)	\(69\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(ln(2))+(6*x^3+8*x^2-30*x+1)*exp(x^3+2*x^2-15*x)^2+(-6*x^4+16*x^3+62*x^2-124*x+8)*exp(x^3+2*x^2-15*x)+3*
x^2-14*x+17,x,method=_RETURNVERBOSE)

[Out]

x*ln(ln(2))+exp(2*(x-3)*(5+x)*x)*x+(-2*x^2+8*x)*exp((x-3)*(5+x)*x)+x^3-7*x^2+17*x

________________________________________________________________________________________

maxima [B]  time = 0.39, size = 56, normalized size = 2.24 \begin {gather*} x^{3} - 7 \, x^{2} + x e^{\left (2 \, x^{3} + 4 \, x^{2} - 30 \, x\right )} - 2 \, {\left (x^{2} - 4 \, x\right )} e^{\left (x^{3} + 2 \, x^{2} - 15 \, x\right )} + x \log \left (\log \relax (2)\right ) + 17 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(2))+(6*x^3+8*x^2-30*x+1)*exp(x^3+2*x^2-15*x)^2+(-6*x^4+16*x^3+62*x^2-124*x+8)*exp(x^3+2*x^2-
15*x)+3*x^2-14*x+17,x, algorithm="maxima")

[Out]

x^3 - 7*x^2 + x*e^(2*x^3 + 4*x^2 - 30*x) - 2*(x^2 - 4*x)*e^(x^3 + 2*x^2 - 15*x) + x*log(log(2)) + 17*x

________________________________________________________________________________________

mupad [B]  time = 0.13, size = 68, normalized size = 2.72 \begin {gather*} 17\,x+8\,x\,{\mathrm {e}}^{x^3+2\,x^2-15\,x}+x\,\ln \left (\ln \relax (2)\right )-7\,x^2+x^3+x\,{\mathrm {e}}^{2\,x^3+4\,x^2-30\,x}-2\,x^2\,{\mathrm {e}}^{x^3+2\,x^2-15\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(log(2)) - 14*x + exp(4*x^2 - 30*x + 2*x^3)*(8*x^2 - 30*x + 6*x^3 + 1) + 3*x^2 + exp(2*x^2 - 15*x + x^3
)*(62*x^2 - 124*x + 16*x^3 - 6*x^4 + 8) + 17,x)

[Out]

17*x + 8*x*exp(2*x^2 - 15*x + x^3) + x*log(log(2)) - 7*x^2 + x^3 + x*exp(4*x^2 - 30*x + 2*x^3) - 2*x^2*exp(2*x
^2 - 15*x + x^3)

________________________________________________________________________________________

sympy [B]  time = 0.16, size = 54, normalized size = 2.16 \begin {gather*} x^{3} - 7 x^{2} + x e^{2 x^{3} + 4 x^{2} - 30 x} + x \left (\log {\left (\log {\relax (2 )} \right )} + 17\right ) + \left (- 2 x^{2} + 8 x\right ) e^{x^{3} + 2 x^{2} - 15 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(ln(2))+(6*x**3+8*x**2-30*x+1)*exp(x**3+2*x**2-15*x)**2+(-6*x**4+16*x**3+62*x**2-124*x+8)*exp(x**3
+2*x**2-15*x)+3*x**2-14*x+17,x)

[Out]

x**3 - 7*x**2 + x*exp(2*x**3 + 4*x**2 - 30*x) + x*(log(log(2)) + 17) + (-2*x**2 + 8*x)*exp(x**3 + 2*x**2 - 15*
x)

________________________________________________________________________________________