3.61.35 \(\int \frac {-e^x-x+e^{4+x+8 x^2} (-6+9 x+144 x^2+e^x (3+144 x))+e^{4+x+8 x^2} (2+e^x (-4-96 x)-6 x-96 x^2) \log (e^x+x)+e^{4+x+8 x^2} (x+16 x^2+e^x (1+16 x)) \log ^2(e^x+x)}{e^x+x} \, dx\)

Optimal. Leaf size=25 \[ -x+e^{4+x+8 x^2} \left (-3+\log \left (e^x+x\right )\right )^2 \]

________________________________________________________________________________________

Rubi [F]  time = 17.60, 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 \frac {-e^x-x+e^{4+x+8 x^2} \left (-6+9 x+144 x^2+e^x (3+144 x)\right )+e^{4+x+8 x^2} \left (2+e^x (-4-96 x)-6 x-96 x^2\right ) \log \left (e^x+x\right )+e^{4+x+8 x^2} \left (x+16 x^2+e^x (1+16 x)\right ) \log ^2\left (e^x+x\right )}{e^x+x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-E^x - x + E^(4 + x + 8*x^2)*(-6 + 9*x + 144*x^2 + E^x*(3 + 144*x)) + E^(4 + x + 8*x^2)*(2 + E^x*(-4 - 96
*x) - 6*x - 96*x^2)*Log[E^x + x] + E^(4 + x + 8*x^2)*(x + 16*x^2 + E^x*(1 + 16*x))*Log[E^x + x]^2)/(E^x + x),x
]

[Out]

9*E^(4 + x + 8*x^2) + E^(127/32 + (1/(4*Sqrt[2]) + 2*Sqrt[2]*x)^2)/8 - x - (E^(127/32)*Sqrt[Pi/2]*(1 + 16*x)*E
rfi[1/(4*Sqrt[2]) + 2*Sqrt[2]*x])/32 - 6*E^(4 + x + 8*x^2)*Log[E^x + x] + (E^(127/32)*Sqrt[Pi/2]*Erfi[(1 + 16*
x)/(4*Sqrt[2])]*Log[E^x + x])/2 + 2*Log[E^x + x]*Defer[Int][E^(4 + x + 8*x^2)/(E^x + x), x] - 2*Log[E^x + x]*D
efer[Int][(E^(4 + x + 8*x^2)*x)/(E^x + x), x] + (E^(127/32)*Sqrt[Pi/2]*Defer[Int][Erfi[1/(4*Sqrt[2]) + 2*Sqrt[
2]*x]/(-E^x - x), x])/2 + (E^(127/32)*Sqrt[Pi/2]*Defer[Int][(x*Erfi[1/(4*Sqrt[2]) + 2*Sqrt[2]*x])/(E^x + x), x
])/2 + Defer[Int][E^(4 + x + 8*x^2)*Log[E^x + x]^2, x] + 16*Defer[Int][E^(4 + x + 8*x^2)*x*Log[E^x + x]^2, x]
- 2*Defer[Int][Defer[Int][E^(4 + x + 8*x^2)/(E^x + x), x], x] - 2*Defer[Int][Defer[Int][E^(4 + x + 8*x^2)/(E^x
+ x), x]/(E^x + x), x] + 2*Defer[Int][(x*Defer[Int][E^(4 + x + 8*x^2)/(E^x + x), x])/(E^x + x), x] + 2*Defer[
Int][Defer[Int][(E^(4 + x + 8*x^2)*x)/(E^x + x), x], x] + 2*Defer[Int][Defer[Int][(E^(4 + x + 8*x^2)*x)/(E^x +
x), x]/(E^x + x), x] - 2*Defer[Int][(x*Defer[Int][(E^(4 + x + 8*x^2)*x)/(E^x + x), x])/(E^x + x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {e^{4+x+8 x^2} \left (-3+\log \left (e^x+x\right )\right ) \left (2-e^x-3 x-48 e^x x-48 x^2+e^x \log \left (e^x+x\right )+x \log \left (e^x+x\right )+16 e^x x \log \left (e^x+x\right )+16 x^2 \log \left (e^x+x\right )\right )}{e^x+x}\right ) \, dx\\ &=-x+\int \frac {e^{4+x+8 x^2} \left (-3+\log \left (e^x+x\right )\right ) \left (2-e^x-3 x-48 e^x x-48 x^2+e^x \log \left (e^x+x\right )+x \log \left (e^x+x\right )+16 e^x x \log \left (e^x+x\right )+16 x^2 \log \left (e^x+x\right )\right )}{e^x+x} \, dx\\ &=-x+\int \frac {e^{4+x+8 x^2} \left (3-\log \left (e^x+x\right )\right ) \left (-2+3 x+48 x^2+e^x (1+48 x)-\left (e^x+x\right ) (1+16 x) \log \left (e^x+x\right )\right )}{e^x+x} \, dx\\ &=-x+\int \left (-\frac {2 e^{4+x+8 x^2} (-1+x) \left (-3+\log \left (e^x+x\right )\right )}{e^x+x}+e^{4+x+8 x^2} \left (-3+\log \left (e^x+x\right )\right ) \left (-1-48 x+\log \left (e^x+x\right )+16 x \log \left (e^x+x\right )\right )\right ) \, dx\\ &=-x-2 \int \frac {e^{4+x+8 x^2} (-1+x) \left (-3+\log \left (e^x+x\right )\right )}{e^x+x} \, dx+\int e^{4+x+8 x^2} \left (-3+\log \left (e^x+x\right )\right ) \left (-1-48 x+\log \left (e^x+x\right )+16 x \log \left (e^x+x\right )\right ) \, dx\\ &=-x-2 \int \left (-\frac {e^{4+x+8 x^2} \left (-3+\log \left (e^x+x\right )\right )}{e^x+x}+\frac {e^{4+x+8 x^2} x \left (-3+\log \left (e^x+x\right )\right )}{e^x+x}\right ) \, dx+\int \left (3 e^{4+x+8 x^2} (1+48 x)-4 e^{4+x+8 x^2} (1+24 x) \log \left (e^x+x\right )+e^{4+x+8 x^2} (1+16 x) \log ^2\left (e^x+x\right )\right ) \, dx\\ &=-x+2 \int \frac {e^{4+x+8 x^2} \left (-3+\log \left (e^x+x\right )\right )}{e^x+x} \, dx-2 \int \frac {e^{4+x+8 x^2} x \left (-3+\log \left (e^x+x\right )\right )}{e^x+x} \, dx+3 \int e^{4+x+8 x^2} (1+48 x) \, dx-4 \int e^{4+x+8 x^2} (1+24 x) \log \left (e^x+x\right ) \, dx+\int e^{4+x+8 x^2} (1+16 x) \log ^2\left (e^x+x\right ) \, dx\\ &=9 e^{4+x+8 x^2}-x-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+\frac {1}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right ) \log \left (e^x+x\right )+2 \int \left (-\frac {3 e^{4+x+8 x^2}}{e^x+x}+\frac {e^{4+x+8 x^2} \log \left (e^x+x\right )}{e^x+x}\right ) \, dx-2 \int \left (-\frac {3 e^{4+x+8 x^2} x}{e^x+x}+\frac {e^{4+x+8 x^2} x \log \left (e^x+x\right )}{e^x+x}\right ) \, dx+4 \int \frac {\left (1+e^x\right ) \left (24 e^{4+x+8 x^2}-e^{127/32} \sqrt {2 \pi } \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right )\right )}{16 \left (e^x+x\right )} \, dx-6 \int e^{4+x+8 x^2} \, dx+\int \left (e^{4+x+8 x^2} \log ^2\left (e^x+x\right )+16 e^{4+x+8 x^2} x \log ^2\left (e^x+x\right )\right ) \, dx\\ &=9 e^{4+x+8 x^2}-x-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+\frac {1}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right ) \log \left (e^x+x\right )+\frac {1}{4} \int \frac {\left (1+e^x\right ) \left (24 e^{4+x+8 x^2}-e^{127/32} \sqrt {2 \pi } \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right )\right )}{e^x+x} \, dx+2 \int \frac {e^{4+x+8 x^2} \log \left (e^x+x\right )}{e^x+x} \, dx-2 \int \frac {e^{4+x+8 x^2} x \log \left (e^x+x\right )}{e^x+x} \, dx-6 \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx+6 \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+16 \int e^{4+x+8 x^2} x \log ^2\left (e^x+x\right ) \, dx-\left (6 e^{127/32}\right ) \int e^{\frac {1}{32} (1+16 x)^2} \, dx+\int e^{4+x+8 x^2} \log ^2\left (e^x+x\right ) \, dx\\ &=9 e^{4+x+8 x^2}-x-\frac {3}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right )-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+\frac {1}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right ) \log \left (e^x+x\right )+\frac {1}{4} \int \left (\frac {24 e^{4+x+8 x^2} \left (1+e^x\right )}{e^x+x}+\frac {e^{127/32} \left (-1-e^x\right ) \sqrt {2 \pi } \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )}{e^x+x}\right ) \, dx-2 \int \frac {\left (1+e^x\right ) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x} \, dx+2 \int \frac {\left (1+e^x\right ) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x} \, dx-6 \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx+6 \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+16 \int e^{4+x+8 x^2} x \log ^2\left (e^x+x\right ) \, dx+\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx-\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+\int e^{4+x+8 x^2} \log ^2\left (e^x+x\right ) \, dx\\ &=9 e^{4+x+8 x^2}-x-\frac {3}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right )-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+\frac {1}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right ) \log \left (e^x+x\right )-2 \int \left (\int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx-\frac {(-1+x) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x}\right ) \, dx+2 \int \left (\int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx-\frac {(-1+x) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x}\right ) \, dx-6 \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx+6 \int \frac {e^{4+x+8 x^2} \left (1+e^x\right )}{e^x+x} \, dx+6 \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+16 \int e^{4+x+8 x^2} x \log ^2\left (e^x+x\right ) \, dx+\frac {1}{2} \left (e^{127/32} \sqrt {\frac {\pi }{2}}\right ) \int \frac {\left (-1-e^x\right ) \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )}{e^x+x} \, dx+\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx-\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+\int e^{4+x+8 x^2} \log ^2\left (e^x+x\right ) \, dx\\ &=9 e^{4+x+8 x^2}-x-\frac {3}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right )-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+\frac {1}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right ) \log \left (e^x+x\right )-2 \int \left (\int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx\right ) \, dx+2 \int \frac {(-1+x) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x} \, dx+2 \int \left (\int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx\right ) \, dx-2 \int \frac {(-1+x) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x} \, dx-6 \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx+6 \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+6 \int \left (e^{4+x+8 x^2}-\frac {e^{4+x+8 x^2} (-1+x)}{e^x+x}\right ) \, dx+16 \int e^{4+x+8 x^2} x \log ^2\left (e^x+x\right ) \, dx+\frac {1}{2} \left (e^{127/32} \sqrt {\frac {\pi }{2}}\right ) \int \left (-\text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )+\frac {(-1+x) \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )}{e^x+x}\right ) \, dx+\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx-\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+\int e^{4+x+8 x^2} \log ^2\left (e^x+x\right ) \, dx\\ &=9 e^{4+x+8 x^2}-x-\frac {3}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right )-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+\frac {1}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right ) \log \left (e^x+x\right )-2 \int \left (\int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx\right ) \, dx+2 \int \left (-\frac {\int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x}+\frac {x \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x}\right ) \, dx+2 \int \left (\int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx\right ) \, dx-2 \int \left (-\frac {\int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x}+\frac {x \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x}\right ) \, dx+6 \int e^{4+x+8 x^2} \, dx-6 \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx-6 \int \frac {e^{4+x+8 x^2} (-1+x)}{e^x+x} \, dx+6 \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+16 \int e^{4+x+8 x^2} x \log ^2\left (e^x+x\right ) \, dx-\frac {1}{2} \left (e^{127/32} \sqrt {\frac {\pi }{2}}\right ) \int \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right ) \, dx+\frac {1}{2} \left (e^{127/32} \sqrt {\frac {\pi }{2}}\right ) \int \frac {(-1+x) \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )}{e^x+x} \, dx+\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx-\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+\int e^{4+x+8 x^2} \log ^2\left (e^x+x\right ) \, dx\\ &=9 e^{4+x+8 x^2}+\frac {1}{8} e^{\frac {127}{32}+\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )^2}-x-\frac {3}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right )-\frac {1}{32} e^{127/32} \sqrt {\frac {\pi }{2}} (1+16 x) \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+\frac {1}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right ) \log \left (e^x+x\right )-2 \int \left (\int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx\right ) \, dx-2 \int \frac {\int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x} \, dx+2 \int \frac {x \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x} \, dx+2 \int \left (\int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx\right ) \, dx+2 \int \frac {\int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x} \, dx-2 \int \frac {x \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x} \, dx-6 \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx+6 \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx-6 \int \left (-\frac {e^{4+x+8 x^2}}{e^x+x}+\frac {e^{4+x+8 x^2} x}{e^x+x}\right ) \, dx+16 \int e^{4+x+8 x^2} x \log ^2\left (e^x+x\right ) \, dx+\left (6 e^{127/32}\right ) \int e^{\frac {1}{32} (1+16 x)^2} \, dx+\frac {1}{2} \left (e^{127/32} \sqrt {\frac {\pi }{2}}\right ) \int \left (\frac {\text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )}{-e^x-x}+\frac {x \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )}{e^x+x}\right ) \, dx+\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx-\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+\int e^{4+x+8 x^2} \log ^2\left (e^x+x\right ) \, dx\\ &=9 e^{4+x+8 x^2}+\frac {1}{8} e^{\frac {127}{32}+\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )^2}-x-\frac {1}{32} e^{127/32} \sqrt {\frac {\pi }{2}} (1+16 x) \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+\frac {1}{2} e^{127/32} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {1+16 x}{4 \sqrt {2}}\right ) \log \left (e^x+x\right )-2 \int \left (\int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx\right ) \, dx-2 \int \frac {\int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x} \, dx+2 \int \frac {x \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx}{e^x+x} \, dx+2 \int \left (\int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx\right ) \, dx+2 \int \frac {\int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x} \, dx-2 \int \frac {x \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx}{e^x+x} \, dx+16 \int e^{4+x+8 x^2} x \log ^2\left (e^x+x\right ) \, dx+\frac {1}{2} \left (e^{127/32} \sqrt {\frac {\pi }{2}}\right ) \int \frac {\text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )}{-e^x-x} \, dx+\frac {1}{2} \left (e^{127/32} \sqrt {\frac {\pi }{2}}\right ) \int \frac {x \text {erfi}\left (\frac {1}{4 \sqrt {2}}+2 \sqrt {2} x\right )}{e^x+x} \, dx+\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2}}{e^x+x} \, dx-\left (2 \log \left (e^x+x\right )\right ) \int \frac {e^{4+x+8 x^2} x}{e^x+x} \, dx+\int e^{4+x+8 x^2} \log ^2\left (e^x+x\right ) \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.13, size = 53, normalized size = 2.12 \begin {gather*} 9 e^{4+x+8 x^2}-x-6 e^{4+x+8 x^2} \log \left (e^x+x\right )+e^{4+x+8 x^2} \log ^2\left (e^x+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-E^x - x + E^(4 + x + 8*x^2)*(-6 + 9*x + 144*x^2 + E^x*(3 + 144*x)) + E^(4 + x + 8*x^2)*(2 + E^x*(-
4 - 96*x) - 6*x - 96*x^2)*Log[E^x + x] + E^(4 + x + 8*x^2)*(x + 16*x^2 + E^x*(1 + 16*x))*Log[E^x + x]^2)/(E^x
+ x),x]

[Out]

9*E^(4 + x + 8*x^2) - x - 6*E^(4 + x + 8*x^2)*Log[E^x + x] + E^(4 + x + 8*x^2)*Log[E^x + x]^2

________________________________________________________________________________________

fricas [B]  time = 0.75, size = 48, normalized size = 1.92 \begin {gather*} e^{\left (8 \, x^{2} + x + 4\right )} \log \left (x + e^{x}\right )^{2} - 6 \, e^{\left (8 \, x^{2} + x + 4\right )} \log \left (x + e^{x}\right ) - x + 9 \, e^{\left (8 \, x^{2} + x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x+1)*exp(x)+16*x^2+x)*exp(8*x^2+x+4)*log(exp(x)+x)^2+((-96*x-4)*exp(x)-96*x^2-6*x+2)*exp(8*x^2
+x+4)*log(exp(x)+x)+((144*x+3)*exp(x)+144*x^2+9*x-6)*exp(8*x^2+x+4)-exp(x)-x)/(exp(x)+x),x, algorithm="fricas"
)

[Out]

e^(8*x^2 + x + 4)*log(x + e^x)^2 - 6*e^(8*x^2 + x + 4)*log(x + e^x) - x + 9*e^(8*x^2 + x + 4)

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (16 \, x^{2} + {\left (16 \, x + 1\right )} e^{x} + x\right )} e^{\left (8 \, x^{2} + x + 4\right )} \log \left (x + e^{x}\right )^{2} - 2 \, {\left (48 \, x^{2} + 2 \, {\left (24 \, x + 1\right )} e^{x} + 3 \, x - 1\right )} e^{\left (8 \, x^{2} + x + 4\right )} \log \left (x + e^{x}\right ) + 3 \, {\left (48 \, x^{2} + {\left (48 \, x + 1\right )} e^{x} + 3 \, x - 2\right )} e^{\left (8 \, x^{2} + x + 4\right )} - x - e^{x}}{x + e^{x}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x+1)*exp(x)+16*x^2+x)*exp(8*x^2+x+4)*log(exp(x)+x)^2+((-96*x-4)*exp(x)-96*x^2-6*x+2)*exp(8*x^2
+x+4)*log(exp(x)+x)+((144*x+3)*exp(x)+144*x^2+9*x-6)*exp(8*x^2+x+4)-exp(x)-x)/(exp(x)+x),x, algorithm="giac")

[Out]

integrate(((16*x^2 + (16*x + 1)*e^x + x)*e^(8*x^2 + x + 4)*log(x + e^x)^2 - 2*(48*x^2 + 2*(24*x + 1)*e^x + 3*x
- 1)*e^(8*x^2 + x + 4)*log(x + e^x) + 3*(48*x^2 + (48*x + 1)*e^x + 3*x - 2)*e^(8*x^2 + x + 4) - x - e^x)/(x +
e^x), x)

________________________________________________________________________________________

maple [B]  time = 0.04, size = 49, normalized size = 1.96

method	result	size
risch	\({\mathrm e}^{8 x^{2}+x +4} \ln \left ({\mathrm e}^{x}+x \right )^{2}-6 \,{\mathrm e}^{8 x^{2}+x +4} \ln \left ({\mathrm e}^{x}+x \right )-x +9 \,{\mathrm e}^{8 x^{2}+x +4}\)	\(49\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((16*x+1)*exp(x)+16*x^2+x)*exp(8*x^2+x+4)*ln(exp(x)+x)^2+((-96*x-4)*exp(x)-96*x^2-6*x+2)*exp(8*x^2+x+4)*l
n(exp(x)+x)+((144*x+3)*exp(x)+144*x^2+9*x-6)*exp(8*x^2+x+4)-exp(x)-x)/(exp(x)+x),x,method=_RETURNVERBOSE)

[Out]

exp(8*x^2+x+4)*ln(exp(x)+x)^2-6*exp(8*x^2+x+4)*ln(exp(x)+x)-x+9*exp(8*x^2+x+4)

________________________________________________________________________________________

maxima [B]  time = 0.38, size = 48, normalized size = 1.92 \begin {gather*} e^{\left (8 \, x^{2} + x + 4\right )} \log \left (x + e^{x}\right )^{2} - 6 \, e^{\left (8 \, x^{2} + x + 4\right )} \log \left (x + e^{x}\right ) - x + 9 \, e^{\left (8 \, x^{2} + x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x+1)*exp(x)+16*x^2+x)*exp(8*x^2+x+4)*log(exp(x)+x)^2+((-96*x-4)*exp(x)-96*x^2-6*x+2)*exp(8*x^2
+x+4)*log(exp(x)+x)+((144*x+3)*exp(x)+144*x^2+9*x-6)*exp(8*x^2+x+4)-exp(x)-x)/(exp(x)+x),x, algorithm="maxima"
)

[Out]

e^(8*x^2 + x + 4)*log(x + e^x)^2 - 6*e^(8*x^2 + x + 4)*log(x + e^x) - x + 9*e^(8*x^2 + x + 4)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int \frac {-{\mathrm {e}}^{8\,x^2+x+4}\,\left (x+{\mathrm {e}}^x\,\left (16\,x+1\right )+16\,x^2\right )\,{\ln \left (x+{\mathrm {e}}^x\right )}^2+{\mathrm {e}}^{8\,x^2+x+4}\,\left (6\,x+{\mathrm {e}}^x\,\left (96\,x+4\right )+96\,x^2-2\right )\,\ln \left (x+{\mathrm {e}}^x\right )+x+{\mathrm {e}}^x-{\mathrm {e}}^{8\,x^2+x+4}\,\left (9\,x+{\mathrm {e}}^x\,\left (144\,x+3\right )+144\,x^2-6\right )}{x+{\mathrm {e}}^x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x + exp(x) - exp(x + 8*x^2 + 4)*(9*x + exp(x)*(144*x + 3) + 144*x^2 - 6) + log(x + exp(x))*exp(x + 8*x^2
+ 4)*(6*x + exp(x)*(96*x + 4) + 96*x^2 - 2) - log(x + exp(x))^2*exp(x + 8*x^2 + 4)*(x + exp(x)*(16*x + 1) + 1
6*x^2))/(x + exp(x)),x)

[Out]

-int((x + exp(x) - exp(x + 8*x^2 + 4)*(9*x + exp(x)*(144*x + 3) + 144*x^2 - 6) + log(x + exp(x))*exp(x + 8*x^2
+ 4)*(6*x + exp(x)*(96*x + 4) + 96*x^2 - 2) - log(x + exp(x))^2*exp(x + 8*x^2 + 4)*(x + exp(x)*(16*x + 1) + 1
6*x^2))/(x + exp(x)), x)

________________________________________________________________________________________

sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x+1)*exp(x)+16*x**2+x)*exp(8*x**2+x+4)*ln(exp(x)+x)**2+((-96*x-4)*exp(x)-96*x**2-6*x+2)*exp(8*
x**2+x+4)*ln(exp(x)+x)+((144*x+3)*exp(x)+144*x**2+9*x-6)*exp(8*x**2+x+4)-exp(x)-x)/(exp(x)+x),x)

[Out]

Timed out

________________________________________________________________________________________