3.38.38 \(\int \frac {-32-32 e^5-32 x+e^x (e^{10} (-160+40 e)-160 x-160 x^2+e (40 x+40 x^2)+e^5 (-160-320 x+e (40+80 x)))}{16 e^5+16 x+e^x ((160-40 e) e^{10}+160 x^2-40 e x^2+e^5 (320 x-80 e x))+e^{2 x} (e^{15} (450-200 e+25 e^2)+450 x^3-200 e x^3+25 e^2 x^3+e^{10} (1350 x-600 e x+75 e^2 x)+e^5 (1350 x^2-600 e x^2+75 e^2 x^2))} \, dx\)

Optimal. Leaf size=24 \[ \log \left (2+\left (-4+e-\frac {4 e^{-x}}{5 \left (e^5+x\right )}\right )^2\right ) \]

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Rubi [F]  time = 7.95, 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 {-32-32 e^5-32 x+e^x \left (e^{10} (-160+40 e)-160 x-160 x^2+e \left (40 x+40 x^2\right )+e^5 (-160-320 x+e (40+80 x))\right )}{16 e^5+16 x+e^x \left ((160-40 e) e^{10}+160 x^2-40 e x^2+e^5 (320 x-80 e x)\right )+e^{2 x} \left (e^{15} \left (450-200 e+25 e^2\right )+450 x^3-200 e x^3+25 e^2 x^3+e^{10} \left (1350 x-600 e x+75 e^2 x\right )+e^5 \left (1350 x^2-600 e x^2+75 e^2 x^2\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-32 - 32*E^5 - 32*x + E^x*(E^10*(-160 + 40*E) - 160*x - 160*x^2 + E*(40*x + 40*x^2) + E^5*(-160 - 320*x +
E*(40 + 80*x))))/(16*E^5 + 16*x + E^x*((160 - 40*E)*E^10 + 160*x^2 - 40*E*x^2 + E^5*(320*x - 80*E*x)) + E^(2*
x)*(E^15*(450 - 200*E + 25*E^2) + 450*x^3 - 200*E*x^3 + 25*E^2*x^3 + E^10*(1350*x - 600*E*x + 75*E^2*x) + E^5*
(1350*x^2 - 600*E*x^2 + 75*E^2*x^2))),x]

[Out]

32*Defer[Int][(-16 - 160*(1 - E/4)*E^(5 + x) - 450*E^(10 + 2*x)*(1 + ((-8 + E)*E)/18) - 160*(1 - E/4)*E^x*x -
900*E^(5 + 2*x)*(1 + ((-8 + E)*E)/18)*x - 450*E^(2*x)*(1 + ((-8 + E)*E)/18)*x^2)^(-1), x] - 40*(4 - E)*Defer[I
nt][E^x/(16 + 160*(1 - E/4)*E^(5 + x) + 450*E^(10 + 2*x)*(1 + ((-8 + E)*E)/18) + 160*(1 - E/4)*E^x*x + 900*E^(
5 + 2*x)*(1 + ((-8 + E)*E)/18)*x + 450*E^(2*x)*(1 + ((-8 + E)*E)/18)*x^2), x] - 40*(4 - E)*Defer[Int][E^(5 + x
)/(16 + 160*(1 - E/4)*E^(5 + x) + 450*E^(10 + 2*x)*(1 + ((-8 + E)*E)/18) + 160*(1 - E/4)*E^x*x + 900*E^(5 + 2*
x)*(1 + ((-8 + E)*E)/18)*x + 450*E^(2*x)*(1 + ((-8 + E)*E)/18)*x^2), x] + 32*Defer[Int][1/((-E^5 - x)*(16 + 16
0*(1 - E/4)*E^(5 + x) + 450*E^(10 + 2*x)*(1 + ((-8 + E)*E)/18) + 160*(1 - E/4)*E^x*x + 900*E^(5 + 2*x)*(1 + ((
-8 + E)*E)/18)*x + 450*E^(2*x)*(1 + ((-8 + E)*E)/18)*x^2)), x] - 40*(4 - E)*Defer[Int][E^(5 + x)/((-E^5 - x)*(
16 + 160*(1 - E/4)*E^(5 + x) + 450*E^(10 + 2*x)*(1 + ((-8 + E)*E)/18) + 160*(1 - E/4)*E^x*x + 900*E^(5 + 2*x)*
(1 + ((-8 + E)*E)/18)*x + 450*E^(2*x)*(1 + ((-8 + E)*E)/18)*x^2)), x] - 40*(4 - E)*Defer[Int][(E^x*x)/(16 + 16
0*(1 - E/4)*E^(5 + x) + 450*E^(10 + 2*x)*(1 + ((-8 + E)*E)/18) + 160*(1 - E/4)*E^x*x + 900*E^(5 + 2*x)*(1 + ((
-8 + E)*E)/18)*x + 450*E^(2*x)*(1 + ((-8 + E)*E)/18)*x^2), x] - 40*(4 - E)*Defer[Int][E^(5 + x)/((E^5 + x)*(16
+ 160*(1 - E/4)*E^(5 + x) + 450*E^(10 + 2*x)*(1 + ((-8 + E)*E)/18) + 160*(1 - E/4)*E^x*x + 900*E^(5 + 2*x)*(1
+ ((-8 + E)*E)/18)*x + 450*E^(2*x)*(1 + ((-8 + E)*E)/18)*x^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 \left (1+e^5+x\right ) \left (-4-20 \left (1-\frac {e}{4}\right ) e^{5+x}-20 \left (1-\frac {e}{4}\right ) e^x x\right )}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{2 (5+x)} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx\\ &=8 \int \frac {\left (1+e^5+x\right ) \left (-4-20 \left (1-\frac {e}{4}\right ) e^{5+x}-20 \left (1-\frac {e}{4}\right ) e^x x\right )}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{2 (5+x)} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx\\ &=8 \int \left (\frac {-4-20 \left (1-\frac {e}{4}\right ) e^{5+x}-20 \left (1-\frac {e}{4}\right ) e^x x}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2}+\frac {-4-20 \left (1-\frac {e}{4}\right ) e^{5+x}-20 \left (1-\frac {e}{4}\right ) e^x x}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )}\right ) \, dx\\ &=8 \int \frac {-4-20 \left (1-\frac {e}{4}\right ) e^{5+x}-20 \left (1-\frac {e}{4}\right ) e^x x}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx+8 \int \frac {-4-20 \left (1-\frac {e}{4}\right ) e^{5+x}-20 \left (1-\frac {e}{4}\right ) e^x x}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx\\ &=8 \int \left (\frac {4}{-16-160 \left (1-\frac {e}{4}\right ) e^{5+x}-450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )-160 \left (1-\frac {e}{4}\right ) e^x x-900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x-450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2}+\frac {5 (-4+e) e^{5+x}}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2}+\frac {5 (-4+e) e^x x}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2}\right ) \, dx+8 \int \left (\frac {4}{\left (-e^5-x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )}+\frac {5 (-4+e) e^{5+x}}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )}+\frac {5 (-4+e) e^x x}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )}\right ) \, dx\\ &=32 \int \frac {1}{-16-160 \left (1-\frac {e}{4}\right ) e^{5+x}-450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )-160 \left (1-\frac {e}{4}\right ) e^x x-900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x-450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx+32 \int \frac {1}{\left (-e^5-x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx-(40 (4-e)) \int \frac {e^{5+x}}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx-(40 (4-e)) \int \frac {e^x x}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx-(40 (4-e)) \int \frac {e^{5+x}}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx-(40 (4-e)) \int \frac {e^x x}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx\\ &=32 \int \frac {1}{-16-160 \left (1-\frac {e}{4}\right ) e^{5+x}-450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )-160 \left (1-\frac {e}{4}\right ) e^x x-900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x-450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx+32 \int \frac {1}{\left (-e^5-x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx-(40 (4-e)) \int \frac {e^{5+x}}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx-(40 (4-e)) \int \frac {e^x x}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx-(40 (4-e)) \int \frac {e^{5+x}}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx-(40 (4-e)) \int \left (\frac {e^x}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2}+\frac {e^{5+x}}{\left (-e^5-x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )}\right ) \, dx\\ &=32 \int \frac {1}{-16-160 \left (1-\frac {e}{4}\right ) e^{5+x}-450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )-160 \left (1-\frac {e}{4}\right ) e^x x-900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x-450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx+32 \int \frac {1}{\left (-e^5-x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx-(40 (4-e)) \int \frac {e^x}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx-(40 (4-e)) \int \frac {e^{5+x}}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx-(40 (4-e)) \int \frac {e^{5+x}}{\left (-e^5-x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx-(40 (4-e)) \int \frac {e^x x}{16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2} \, dx-(40 (4-e)) \int \frac {e^{5+x}}{\left (e^5+x\right ) \left (16+160 \left (1-\frac {e}{4}\right ) e^{5+x}+450 e^{10+2 x} \left (1+\frac {1}{18} (-8+e) e\right )+160 \left (1-\frac {e}{4}\right ) e^x x+900 e^{5+2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x+450 e^{2 x} \left (1+\frac {1}{18} (-8+e) e\right ) x^2\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.13, size = 144, normalized size = 6.00 \begin {gather*} 8 \left (-\frac {x}{4}-\frac {1}{4} \log \left (e^5+x\right )+\frac {1}{8} \log \left (16+160 e^{5+x}-40 e^{6+x}+450 e^{10+2 x}-200 e^{11+2 x}+25 e^{12+2 x}+160 e^x x-40 e^{1+x} x+900 e^{5+2 x} x-400 e^{6+2 x} x+50 e^{7+2 x} x+450 e^{2 x} x^2-200 e^{1+2 x} x^2+25 e^{2+2 x} x^2\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-32 - 32*E^5 - 32*x + E^x*(E^10*(-160 + 40*E) - 160*x - 160*x^2 + E*(40*x + 40*x^2) + E^5*(-160 - 3
20*x + E*(40 + 80*x))))/(16*E^5 + 16*x + E^x*((160 - 40*E)*E^10 + 160*x^2 - 40*E*x^2 + E^5*(320*x - 80*E*x)) +
E^(2*x)*(E^15*(450 - 200*E + 25*E^2) + 450*x^3 - 200*E*x^3 + 25*E^2*x^3 + E^10*(1350*x - 600*E*x + 75*E^2*x)
+ E^5*(1350*x^2 - 600*E*x^2 + 75*E^2*x^2))),x]

[Out]

8*(-1/4*x - Log[E^5 + x]/4 + Log[16 + 160*E^(5 + x) - 40*E^(6 + x) + 450*E^(10 + 2*x) - 200*E^(11 + 2*x) + 25*
E^(12 + 2*x) + 160*E^x*x - 40*E^(1 + x)*x + 900*E^(5 + 2*x)*x - 400*E^(6 + 2*x)*x + 50*E^(7 + 2*x)*x + 450*E^(
2*x)*x^2 - 200*E^(1 + 2*x)*x^2 + 25*E^(2 + 2*x)*x^2]/8)

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fricas [B]  time = 0.84, size = 89, normalized size = 3.71 \begin {gather*} -2 \, x + \log \left (\frac {25 \, {\left (x^{2} e^{2} - 8 \, x^{2} e + 18 \, x^{2} + 2 \, x e^{7} - 16 \, x e^{6} + 36 \, x e^{5} + e^{12} - 8 \, e^{11} + 18 \, e^{10}\right )} e^{\left (2 \, x\right )} - 40 \, {\left (x e - 4 \, x + e^{6} - 4 \, e^{5}\right )} e^{x} + 16}{x^{2} + 2 \, x e^{5} + e^{10}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((40*exp(1)-160)*exp(5)^2+((80*x+40)*exp(1)-320*x-160)*exp(5)+(40*x^2+40*x)*exp(1)-160*x^2-160*x)*e
xp(x)-32*exp(5)-32*x-32)/(((25*exp(1)^2-200*exp(1)+450)*exp(5)^3+(75*x*exp(1)^2-600*x*exp(1)+1350*x)*exp(5)^2+
(75*x^2*exp(1)^2-600*x^2*exp(1)+1350*x^2)*exp(5)+25*x^3*exp(1)^2-200*x^3*exp(1)+450*x^3)*exp(x)^2+((-40*exp(1)
+160)*exp(5)^2+(-80*x*exp(1)+320*x)*exp(5)-40*x^2*exp(1)+160*x^2)*exp(x)+16*exp(5)+16*x),x, algorithm="fricas"
)

[Out]

-2*x + log((25*(x^2*e^2 - 8*x^2*e + 18*x^2 + 2*x*e^7 - 16*x*e^6 + 36*x*e^5 + e^12 - 8*e^11 + 18*e^10)*e^(2*x)
- 40*(x*e - 4*x + e^6 - 4*e^5)*e^x + 16)/(x^2 + 2*x*e^5 + e^10))

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giac [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((((40*exp(1)-160)*exp(5)^2+((80*x+40)*exp(1)-320*x-160)*exp(5)+(40*x^2+40*x)*exp(1)-160*x^2-160*x)*e
xp(x)-32*exp(5)-32*x-32)/(((25*exp(1)^2-200*exp(1)+450)*exp(5)^3+(75*x*exp(1)^2-600*x*exp(1)+1350*x)*exp(5)^2+
(75*x^2*exp(1)^2-600*x^2*exp(1)+1350*x^2)*exp(5)+25*x^3*exp(1)^2-200*x^3*exp(1)+450*x^3)*exp(x)^2+((-40*exp(1)
+160)*exp(5)^2+(-80*x*exp(1)+320*x)*exp(5)-40*x^2*exp(1)+160*x^2)*exp(x)+16*exp(5)+16*x),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.59, size = 92, normalized size = 3.83

method	result	size
risch	\(-2 x +\ln \left ({\mathrm e}^{2 x}-\frac {8 \left ({\mathrm e}-4\right ) {\mathrm e}^{x}}{5 \left ({\mathrm e}^{7}-8 \,{\mathrm e}^{6}+18 \,{\mathrm e}^{5}+{\mathrm e}^{2} x -8 x \,{\mathrm e}+18 x \right )}+\frac {16}{25 \left ({\mathrm e}^{12}-8 \,{\mathrm e}^{11}+18 \,{\mathrm e}^{10}+2 x \,{\mathrm e}^{7}-16 x \,{\mathrm e}^{6}+36 x \,{\mathrm e}^{5}+x^{2} {\mathrm e}^{2}-8 x^{2} {\mathrm e}+18 x^{2}\right )}\right )\)	\(92\)
norman	\(-2 x -2 \ln \left ({\mathrm e}^{5}+x \right )+\ln \left (25 \,{\mathrm e}^{10} {\mathrm e}^{2} {\mathrm e}^{2 x}+50 \,{\mathrm e}^{5} {\mathrm e}^{2} {\mathrm e}^{2 x} x +25 \,{\mathrm e}^{2} {\mathrm e}^{2 x} x^{2}-200 \,{\mathrm e}^{10} {\mathrm e} \,{\mathrm e}^{2 x}-400 \,{\mathrm e}^{5} {\mathrm e} \,{\mathrm e}^{2 x} x -200 \,{\mathrm e} \,{\mathrm e}^{2 x} x^{2}+450 \,{\mathrm e}^{10} {\mathrm e}^{2 x}+900 x \,{\mathrm e}^{5} {\mathrm e}^{2 x}+450 \,{\mathrm e}^{2 x} x^{2}-40 \,{\mathrm e}^{5} {\mathrm e} \,{\mathrm e}^{x}-40 x \,{\mathrm e} \,{\mathrm e}^{x}+160 \,{\mathrm e}^{5} {\mathrm e}^{x}+160 \,{\mathrm e}^{x} x +16\right )\)	\(143\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((40*exp(1)-160)*exp(5)^2+((80*x+40)*exp(1)-320*x-160)*exp(5)+(40*x^2+40*x)*exp(1)-160*x^2-160*x)*exp(x)-
32*exp(5)-32*x-32)/(((25*exp(1)^2-200*exp(1)+450)*exp(5)^3+(75*x*exp(1)^2-600*x*exp(1)+1350*x)*exp(5)^2+(75*x^
2*exp(1)^2-600*x^2*exp(1)+1350*x^2)*exp(5)+25*x^3*exp(1)^2-200*x^3*exp(1)+450*x^3)*exp(x)^2+((-40*exp(1)+160)*
exp(5)^2+(-80*x*exp(1)+320*x)*exp(5)-40*x^2*exp(1)+160*x^2)*exp(x)+16*exp(5)+16*x),x,method=_RETURNVERBOSE)

[Out]

-2*x+ln(exp(2*x)-8/5*(exp(1)-4)/(exp(7)-8*exp(6)+18*exp(5)+exp(2)*x-8*x*exp(1)+18*x)*exp(x)+16/25/(exp(12)-8*e
xp(11)+18*exp(10)+2*x*exp(7)-16*x*exp(6)+36*x*exp(5)+x^2*exp(2)-8*x^2*exp(1)+18*x^2))

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maxima [B]  time = 0.56, size = 108, normalized size = 4.50 \begin {gather*} -2 \, x + \log \left (\frac {25 \, {\left (x^{2} {\left (e^{2} - 8 \, e + 18\right )} + 2 \, x {\left (e^{7} - 8 \, e^{6} + 18 \, e^{5}\right )} + e^{12} - 8 \, e^{11} + 18 \, e^{10}\right )} e^{\left (2 \, x\right )} - 40 \, {\left (x {\left (e - 4\right )} + e^{6} - 4 \, e^{5}\right )} e^{x} + 16}{25 \, {\left (x^{2} {\left (e^{2} - 8 \, e + 18\right )} + 2 \, x {\left (e^{7} - 8 \, e^{6} + 18 \, e^{5}\right )} + e^{12} - 8 \, e^{11} + 18 \, e^{10}\right )}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((40*exp(1)-160)*exp(5)^2+((80*x+40)*exp(1)-320*x-160)*exp(5)+(40*x^2+40*x)*exp(1)-160*x^2-160*x)*e
xp(x)-32*exp(5)-32*x-32)/(((25*exp(1)^2-200*exp(1)+450)*exp(5)^3+(75*x*exp(1)^2-600*x*exp(1)+1350*x)*exp(5)^2+
(75*x^2*exp(1)^2-600*x^2*exp(1)+1350*x^2)*exp(5)+25*x^3*exp(1)^2-200*x^3*exp(1)+450*x^3)*exp(x)^2+((-40*exp(1)
+160)*exp(5)^2+(-80*x*exp(1)+320*x)*exp(5)-40*x^2*exp(1)+160*x^2)*exp(x)+16*exp(5)+16*x),x, algorithm="maxima"
)

[Out]

-2*x + log(1/25*(25*(x^2*(e^2 - 8*e + 18) + 2*x*(e^7 - 8*e^6 + 18*e^5) + e^12 - 8*e^11 + 18*e^10)*e^(2*x) - 40
*(x*(e - 4) + e^6 - 4*e^5)*e^x + 16)/(x^2*(e^2 - 8*e + 18) + 2*x*(e^7 - 8*e^6 + 18*e^5) + e^12 - 8*e^11 + 18*e
^10))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {32\,x+32\,{\mathrm {e}}^5+{\mathrm {e}}^x\,\left (160\,x-\mathrm {e}\,\left (40\,x^2+40\,x\right )+160\,x^2-{\mathrm {e}}^{10}\,\left (40\,\mathrm {e}-160\right )+{\mathrm {e}}^5\,\left (320\,x-\mathrm {e}\,\left (80\,x+40\right )+160\right )\right )+32}{16\,x+16\,{\mathrm {e}}^5+{\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^{10}\,\left (1350\,x-600\,x\,\mathrm {e}+75\,x\,{\mathrm {e}}^2\right )+{\mathrm {e}}^5\,\left (75\,x^2\,{\mathrm {e}}^2-600\,x^2\,\mathrm {e}+1350\,x^2\right )-200\,x^3\,\mathrm {e}+25\,x^3\,{\mathrm {e}}^2+{\mathrm {e}}^{15}\,\left (25\,{\mathrm {e}}^2-200\,\mathrm {e}+450\right )+450\,x^3\right )+{\mathrm {e}}^x\,\left ({\mathrm {e}}^5\,\left (320\,x-80\,x\,\mathrm {e}\right )-40\,x^2\,\mathrm {e}+160\,x^2-{\mathrm {e}}^{10}\,\left (40\,\mathrm {e}-160\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(32*x + 32*exp(5) + exp(x)*(160*x - exp(1)*(40*x + 40*x^2) + 160*x^2 - exp(10)*(40*exp(1) - 160) + exp(5)
*(320*x - exp(1)*(80*x + 40) + 160)) + 32)/(16*x + 16*exp(5) + exp(2*x)*(exp(10)*(1350*x - 600*x*exp(1) + 75*x
*exp(2)) + exp(5)*(75*x^2*exp(2) - 600*x^2*exp(1) + 1350*x^2) - 200*x^3*exp(1) + 25*x^3*exp(2) + exp(15)*(25*e
xp(2) - 200*exp(1) + 450) + 450*x^3) + exp(x)*(exp(5)*(320*x - 80*x*exp(1)) - 40*x^2*exp(1) + 160*x^2 - exp(10
)*(40*exp(1) - 160))),x)

[Out]

int(-(32*x + 32*exp(5) + exp(x)*(160*x - exp(1)*(40*x + 40*x^2) + 160*x^2 - exp(10)*(40*exp(1) - 160) + exp(5)
*(320*x - exp(1)*(80*x + 40) + 160)) + 32)/(16*x + 16*exp(5) + exp(2*x)*(exp(10)*(1350*x - 600*x*exp(1) + 75*x
*exp(2)) + exp(5)*(75*x^2*exp(2) - 600*x^2*exp(1) + 1350*x^2) - 200*x^3*exp(1) + 25*x^3*exp(2) + exp(15)*(25*e
xp(2) - 200*exp(1) + 450) + 450*x^3) + exp(x)*(exp(5)*(320*x - 80*x*exp(1)) - 40*x^2*exp(1) + 160*x^2 - exp(10
)*(40*exp(1) - 160))), x)

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sympy [B]  time = 7.21, size = 110, normalized size = 4.58 \begin {gather*} - 2 x + \log {\left (e^{2 x} + \frac {16}{- 200 e x^{2} + 25 x^{2} e^{2} + 450 x^{2} - 400 x e^{6} + 50 x e^{7} + 900 x e^{5} - 200 e^{11} + 25 e^{12} + 450 e^{10}} + \frac {\left (32 - 8 e\right ) e^{x}}{- 40 e x + 5 x e^{2} + 90 x - 40 e^{6} + 5 e^{7} + 90 e^{5}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((40*exp(1)-160)*exp(5)**2+((80*x+40)*exp(1)-320*x-160)*exp(5)+(40*x**2+40*x)*exp(1)-160*x**2-160*x
)*exp(x)-32*exp(5)-32*x-32)/(((25*exp(1)**2-200*exp(1)+450)*exp(5)**3+(75*x*exp(1)**2-600*x*exp(1)+1350*x)*exp
(5)**2+(75*x**2*exp(1)**2-600*x**2*exp(1)+1350*x**2)*exp(5)+25*x**3*exp(1)**2-200*x**3*exp(1)+450*x**3)*exp(x)
**2+((-40*exp(1)+160)*exp(5)**2+(-80*x*exp(1)+320*x)*exp(5)-40*x**2*exp(1)+160*x**2)*exp(x)+16*exp(5)+16*x),x)

[Out]

-2*x + log(exp(2*x) + 16/(-200*E*x**2 + 25*x**2*exp(2) + 450*x**2 - 400*x*exp(6) + 50*x*exp(7) + 900*x*exp(5)
- 200*exp(11) + 25*exp(12) + 450*exp(10)) + (32 - 8*E)*exp(x)/(-40*E*x + 5*x*exp(2) + 90*x - 40*exp(6) + 5*exp
(7) + 90*exp(5)))

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