3.58.29 \(\int \frac {e^x (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 (-64 x^4+32 x^5))+e^{2 x} (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 (-8 x+8 x^2+128 x^5-64 x^6))+e^{3 x} (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} (8 x^3+24 x^6)+e^5 (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7))+e^{4 x} (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} (-8 x^4-8 x^7)+e^5 (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8))+e^{5 x} (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} (x^2+2 x^5+x^8)+e^5 (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9))}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 (-64 x^4+32 x^5)+e^x (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 (128 x^5-64 x^6))+e^{2 x} (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} (8 x^3+24 x^6)+e^5 (-32 x^3+16 x^4-96 x^6+48 x^7))+e^{3 x} (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} (-8 x^4-8 x^7)+e^5 (32 x^4-16 x^5+32 x^7-16 x^8))+e^{4 x} (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} (x^2+2 x^5+x^8)+e^5 (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9))} \, dx\)

Optimal. Leaf size=34 \[ -2+e^x+\frac {1}{\left (-2+e^5+x\right ) \left (x+\left (2 e^{-x} x-x^2\right )^2\right )} \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^x*(64*x^4 + 16*E^10*x^4 - 64*x^5 + 16*x^6 + E^5*(-64*x^4 + 32*x^5)) + E^(2*x)*(16*x - 28*x^2 + 8*x^3 -
128*x^5 - 32*E^10*x^5 + 128*x^6 - 32*x^7 + E^5*(-8*x + 8*x^2 + 128*x^5 - 64*x^6)) + E^(3*x)*(-24*x^2 + 56*x^3
- 36*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 + E^10*(8*x^3 + 24*x^6) + E^5*(12*x^2 - 36*x^3 + 16*x^4 - 96*x^6 +
48*x^7)) + E^(4*x)*(2 - 2*x + 8*x^3 - 37*x^4 + 32*x^5 - 8*x^6 - 32*x^7 + 32*x^8 - 8*x^9 + E^10*(-8*x^4 - 8*x^
7) + E^5*(-1 - 4*x^3 + 32*x^4 - 16*x^5 + 32*x^7 - 16*x^8)) + E^(5*x)*(4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*
x^7 + 4*x^8 - 4*x^9 + x^10 + E^10*(x^2 + 2*x^5 + x^8) + E^5*(-4*x^2 + 2*x^3 - 8*x^5 + 4*x^6 - 4*x^8 + 2*x^9)))
/(64*x^4 + 16*E^10*x^4 - 64*x^5 + 16*x^6 + E^5*(-64*x^4 + 32*x^5) + E^x*(-128*x^5 - 32*E^10*x^5 + 128*x^6 - 32
*x^7 + E^5*(128*x^5 - 64*x^6)) + E^(2*x)*(32*x^3 - 32*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 + E^10*(8*x^3 + 2
4*x^6) + E^5*(-32*x^3 + 16*x^4 - 96*x^6 + 48*x^7)) + E^(3*x)*(-32*x^4 + 32*x^5 - 8*x^6 - 32*x^7 + 32*x^8 - 8*x
^9 + E^10*(-8*x^4 - 8*x^7) + E^5*(32*x^4 - 16*x^5 + 32*x^7 - 16*x^8)) + E^(4*x)*(4*x^2 - 4*x^3 + x^4 + 8*x^5 -
8*x^6 + 2*x^7 + 4*x^8 - 4*x^9 + x^10 + E^10*(x^2 + 2*x^5 + x^8) + E^5*(-4*x^2 + 2*x^3 - 8*x^5 + 4*x^6 - 4*x^8
+ 2*x^9))),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 0.54, size = 114, normalized size = 3.35 \begin {gather*} \frac {e^x \left (4 e^5 x^2+4 (-2+x) x^2-4 e^{5+x} x^3+e^x \left (1+8 x^3-4 x^4\right )+e^{5+2 x} \left (x+x^4\right )+e^{2 x} x \left (-2+x-2 x^3+x^4\right )\right )}{x \left (-2+e^5+x\right ) \left (4 x-4 e^x x^2+e^{2 x} \left (1+x^3\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(64*x^4 + 16*E^10*x^4 - 64*x^5 + 16*x^6 + E^5*(-64*x^4 + 32*x^5)) + E^(2*x)*(16*x - 28*x^2 + 8*
x^3 - 128*x^5 - 32*E^10*x^5 + 128*x^6 - 32*x^7 + E^5*(-8*x + 8*x^2 + 128*x^5 - 64*x^6)) + E^(3*x)*(-24*x^2 + 5
6*x^3 - 36*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 + E^10*(8*x^3 + 24*x^6) + E^5*(12*x^2 - 36*x^3 + 16*x^4 - 96
*x^6 + 48*x^7)) + E^(4*x)*(2 - 2*x + 8*x^3 - 37*x^4 + 32*x^5 - 8*x^6 - 32*x^7 + 32*x^8 - 8*x^9 + E^10*(-8*x^4
- 8*x^7) + E^5*(-1 - 4*x^3 + 32*x^4 - 16*x^5 + 32*x^7 - 16*x^8)) + E^(5*x)*(4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^
6 + 2*x^7 + 4*x^8 - 4*x^9 + x^10 + E^10*(x^2 + 2*x^5 + x^8) + E^5*(-4*x^2 + 2*x^3 - 8*x^5 + 4*x^6 - 4*x^8 + 2*
x^9)))/(64*x^4 + 16*E^10*x^4 - 64*x^5 + 16*x^6 + E^5*(-64*x^4 + 32*x^5) + E^x*(-128*x^5 - 32*E^10*x^5 + 128*x^
6 - 32*x^7 + E^5*(128*x^5 - 64*x^6)) + E^(2*x)*(32*x^3 - 32*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 + E^10*(8*x
^3 + 24*x^6) + E^5*(-32*x^3 + 16*x^4 - 96*x^6 + 48*x^7)) + E^(3*x)*(-32*x^4 + 32*x^5 - 8*x^6 - 32*x^7 + 32*x^8
- 8*x^9 + E^10*(-8*x^4 - 8*x^7) + E^5*(32*x^4 - 16*x^5 + 32*x^7 - 16*x^8)) + E^(4*x)*(4*x^2 - 4*x^3 + x^4 + 8
*x^5 - 8*x^6 + 2*x^7 + 4*x^8 - 4*x^9 + x^10 + E^10*(x^2 + 2*x^5 + x^8) + E^5*(-4*x^2 + 2*x^3 - 8*x^5 + 4*x^6 -
4*x^8 + 2*x^9))),x]

[Out]

(E^x*(4*E^5*x^2 + 4*(-2 + x)*x^2 - 4*E^(5 + x)*x^3 + E^x*(1 + 8*x^3 - 4*x^4) + E^(5 + 2*x)*(x + x^4) + E^(2*x)
*x*(-2 + x - 2*x^3 + x^4)))/(x*(-2 + E^5 + x)*(4*x - 4*E^x*x^2 + E^(2*x)*(1 + x^3)))

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fricas [B]  time = 0.59, size = 141, normalized size = 4.15 \begin {gather*} \frac {{\left (x^{5} - 2 \, x^{4} + x^{2} + {\left (x^{4} + x\right )} e^{5} - 2 \, x\right )} e^{\left (3 \, x\right )} - {\left (4 \, x^{4} + 4 \, x^{3} e^{5} - 8 \, x^{3} - 1\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{3} + x^{2} e^{5} - 2 \, x^{2}\right )} e^{x}}{4 \, x^{3} + 4 \, x^{2} e^{5} - 8 \, x^{2} + {\left (x^{5} - 2 \, x^{4} + x^{2} + {\left (x^{4} + x\right )} e^{5} - 2 \, x\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{4} + x^{3} e^{5} - 2 \, x^{3}\right )} e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+2*x^7-8*x^6
+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^5+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+
32*x^8-32*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-36*x^3+
12*x^2)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^5-36*x^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*
x^2-8*x)*exp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp(5)^2+(32*x^5-64*x^4)*exp(5)+16*
x^6-64*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+
4*x^8+2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4)*exp(
5)-8*x^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)*exp(x)^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*ex
p(5)+24*x^8-96*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5)*exp(5)-32*x^7+128*
x^6-128*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4),x, algorithm="fricas")

[Out]

((x^5 - 2*x^4 + x^2 + (x^4 + x)*e^5 - 2*x)*e^(3*x) - (4*x^4 + 4*x^3*e^5 - 8*x^3 - 1)*e^(2*x) + 4*(x^3 + x^2*e^
5 - 2*x^2)*e^x)/(4*x^3 + 4*x^2*e^5 - 8*x^2 + (x^5 - 2*x^4 + x^2 + (x^4 + x)*e^5 - 2*x)*e^(2*x) - 4*(x^4 + x^3*
e^5 - 2*x^3)*e^x)

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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((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+2*x^7-8*x^6
+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^5+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+
32*x^8-32*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-36*x^3+
12*x^2)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^5-36*x^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*
x^2-8*x)*exp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp(5)^2+(32*x^5-64*x^4)*exp(5)+16*
x^6-64*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+
4*x^8+2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4)*exp(
5)-8*x^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)*exp(x)^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*ex
p(5)+24*x^8-96*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5)*exp(5)-32*x^7+128*
x^6-128*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.27, size = 76, normalized size = 2.24

method	result	size
risch	\(\frac {1}{\left (x^{3} {\mathrm e}^{5}+x^{4}-2 x^{3}+{\mathrm e}^{5}+x -2\right ) x}+{\mathrm e}^{x}+\frac {4 \,{\mathrm e}^{x} x -4}{\left ({\mathrm e}^{5}+x -2\right ) \left (x^{3}+1\right ) \left ({\mathrm e}^{2 x} x^{3}-4 \,{\mathrm e}^{x} x^{2}+{\mathrm e}^{2 x}+4 x \right )}\)	\(76\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+2*x^7-8*x^6+8*x^5
+x^4-4*x^3+4*x^2)*exp(x)^5+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+32*x^8
-32*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-36*x^3+12*x^2
)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^5-36*x^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*x^2-8*
x)*exp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp(5)^2+(32*x^5-64*x^4)*exp(5)+16*x^6-64
*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+
2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4)*exp(5)-8*x
^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)*exp(x)^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*exp(5)+2
4*x^8-96*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5)*exp(5)-32*x^7+128*x^6-12
8*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4),x,method=_RETURNVERBOSE)

[Out]

1/(x^3*exp(5)+x^4-2*x^3+exp(5)+x-2)/x+exp(x)+4*(exp(x)*x-1)/(exp(5)+x-2)/(x^3+1)/(exp(2*x)*x^3-4*exp(x)*x^2+ex
p(2*x)+4*x)

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maxima [B]  time = 0.70, size = 125, normalized size = 3.68 \begin {gather*} \frac {{\left (x^{5} + x^{4} {\left (e^{5} - 2\right )} + x^{2} + x {\left (e^{5} - 2\right )}\right )} e^{\left (3 \, x\right )} - {\left (4 \, x^{4} + 4 \, x^{3} {\left (e^{5} - 2\right )} - 1\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{3} + x^{2} {\left (e^{5} - 2\right )}\right )} e^{x}}{4 \, x^{3} + 4 \, x^{2} {\left (e^{5} - 2\right )} + {\left (x^{5} + x^{4} {\left (e^{5} - 2\right )} + x^{2} + x {\left (e^{5} - 2\right )}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{4} + x^{3} {\left (e^{5} - 2\right )}\right )} e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+2*x^7-8*x^6
+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^5+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+
32*x^8-32*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-36*x^3+
12*x^2)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^5-36*x^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*
x^2-8*x)*exp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp(5)^2+(32*x^5-64*x^4)*exp(5)+16*
x^6-64*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+
4*x^8+2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4)*exp(
5)-8*x^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)*exp(x)^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*ex
p(5)+24*x^8-96*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5)*exp(5)-32*x^7+128*
x^6-128*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4),x, algorithm="maxima")

[Out]

((x^5 + x^4*(e^5 - 2) + x^2 + x*(e^5 - 2))*e^(3*x) - (4*x^4 + 4*x^3*(e^5 - 2) - 1)*e^(2*x) + 4*(x^3 + x^2*(e^5
- 2))*e^x)/(4*x^3 + 4*x^2*(e^5 - 2) + (x^5 + x^4*(e^5 - 2) + x^2 + x*(e^5 - 2))*e^(2*x) - 4*(x^4 + x^3*(e^5 -
2))*e^x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{3\,x}\,\left ({\mathrm {e}}^5\,\left (48\,x^7-96\,x^6+16\,x^4-36\,x^3+12\,x^2\right )+{\mathrm {e}}^{10}\,\left (24\,x^6+8\,x^3\right )-24\,x^2+56\,x^3-36\,x^4+8\,x^5+96\,x^6-96\,x^7+24\,x^8\right )-{\mathrm {e}}^{2\,x}\,\left (32\,x^5\,{\mathrm {e}}^{10}-16\,x+{\mathrm {e}}^5\,\left (64\,x^6-128\,x^5-8\,x^2+8\,x\right )+28\,x^2-8\,x^3+128\,x^5-128\,x^6+32\,x^7\right )-{\mathrm {e}}^{4\,x}\,\left (2\,x+{\mathrm {e}}^5\,\left (16\,x^8-32\,x^7+16\,x^5-32\,x^4+4\,x^3+1\right )+{\mathrm {e}}^{10}\,\left (8\,x^7+8\,x^4\right )-8\,x^3+37\,x^4-32\,x^5+8\,x^6+32\,x^7-32\,x^8+8\,x^9-2\right )+{\mathrm {e}}^x\,\left (16\,x^4\,{\mathrm {e}}^{10}-{\mathrm {e}}^5\,\left (64\,x^4-32\,x^5\right )+64\,x^4-64\,x^5+16\,x^6\right )+{\mathrm {e}}^{5\,x}\,\left ({\mathrm {e}}^{10}\,\left (x^8+2\,x^5+x^2\right )-{\mathrm {e}}^5\,\left (-2\,x^9+4\,x^8-4\,x^6+8\,x^5-2\,x^3+4\,x^2\right )+4\,x^2-4\,x^3+x^4+8\,x^5-8\,x^6+2\,x^7+4\,x^8-4\,x^9+x^{10}\right )}{16\,x^4\,{\mathrm {e}}^{10}-{\mathrm {e}}^5\,\left (64\,x^4-32\,x^5\right )-{\mathrm {e}}^x\,\left (32\,x^5\,{\mathrm {e}}^{10}-{\mathrm {e}}^5\,\left (128\,x^5-64\,x^6\right )+128\,x^5-128\,x^6+32\,x^7\right )+{\mathrm {e}}^{4\,x}\,\left ({\mathrm {e}}^{10}\,\left (x^8+2\,x^5+x^2\right )-{\mathrm {e}}^5\,\left (-2\,x^9+4\,x^8-4\,x^6+8\,x^5-2\,x^3+4\,x^2\right )+4\,x^2-4\,x^3+x^4+8\,x^5-8\,x^6+2\,x^7+4\,x^8-4\,x^9+x^{10}\right )-{\mathrm {e}}^{3\,x}\,\left ({\mathrm {e}}^{10}\,\left (8\,x^7+8\,x^4\right )+32\,x^4-32\,x^5+8\,x^6+32\,x^7-32\,x^8+8\,x^9-{\mathrm {e}}^5\,\left (-16\,x^8+32\,x^7-16\,x^5+32\,x^4\right )\right )+{\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^{10}\,\left (24\,x^6+8\,x^3\right )+32\,x^3-32\,x^4+8\,x^5+96\,x^6-96\,x^7+24\,x^8-{\mathrm {e}}^5\,\left (-48\,x^7+96\,x^6-16\,x^4+32\,x^3\right )\right )+64\,x^4-64\,x^5+16\,x^6} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(3*x)*(exp(5)*(12*x^2 - 36*x^3 + 16*x^4 - 96*x^6 + 48*x^7) + exp(10)*(8*x^3 + 24*x^6) - 24*x^2 + 56*x^
3 - 36*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8) - exp(2*x)*(32*x^5*exp(10) - 16*x + exp(5)*(8*x - 8*x^2 - 128*x
^5 + 64*x^6) + 28*x^2 - 8*x^3 + 128*x^5 - 128*x^6 + 32*x^7) - exp(4*x)*(2*x + exp(5)*(4*x^3 - 32*x^4 + 16*x^5
- 32*x^7 + 16*x^8 + 1) + exp(10)*(8*x^4 + 8*x^7) - 8*x^3 + 37*x^4 - 32*x^5 + 8*x^6 + 32*x^7 - 32*x^8 + 8*x^9 -
2) + exp(x)*(16*x^4*exp(10) - exp(5)*(64*x^4 - 32*x^5) + 64*x^4 - 64*x^5 + 16*x^6) + exp(5*x)*(exp(10)*(x^2 +
2*x^5 + x^8) - exp(5)*(4*x^2 - 2*x^3 + 8*x^5 - 4*x^6 + 4*x^8 - 2*x^9) + 4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 +
2*x^7 + 4*x^8 - 4*x^9 + x^10))/(16*x^4*exp(10) - exp(5)*(64*x^4 - 32*x^5) - exp(x)*(32*x^5*exp(10) - exp(5)*(
128*x^5 - 64*x^6) + 128*x^5 - 128*x^6 + 32*x^7) + exp(4*x)*(exp(10)*(x^2 + 2*x^5 + x^8) - exp(5)*(4*x^2 - 2*x^
3 + 8*x^5 - 4*x^6 + 4*x^8 - 2*x^9) + 4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*x^7 + 4*x^8 - 4*x^9 + x^10) - exp
(3*x)*(exp(10)*(8*x^4 + 8*x^7) + 32*x^4 - 32*x^5 + 8*x^6 + 32*x^7 - 32*x^8 + 8*x^9 - exp(5)*(32*x^4 - 16*x^5 +
32*x^7 - 16*x^8)) + exp(2*x)*(exp(10)*(8*x^3 + 24*x^6) + 32*x^3 - 32*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 -
exp(5)*(32*x^3 - 16*x^4 + 96*x^6 - 48*x^7)) + 64*x^4 - 64*x^5 + 16*x^6),x)

[Out]

int((exp(3*x)*(exp(5)*(12*x^2 - 36*x^3 + 16*x^4 - 96*x^6 + 48*x^7) + exp(10)*(8*x^3 + 24*x^6) - 24*x^2 + 56*x^
3 - 36*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8) - exp(2*x)*(32*x^5*exp(10) - 16*x + exp(5)*(8*x - 8*x^2 - 128*x
^5 + 64*x^6) + 28*x^2 - 8*x^3 + 128*x^5 - 128*x^6 + 32*x^7) - exp(4*x)*(2*x + exp(5)*(4*x^3 - 32*x^4 + 16*x^5
- 32*x^7 + 16*x^8 + 1) + exp(10)*(8*x^4 + 8*x^7) - 8*x^3 + 37*x^4 - 32*x^5 + 8*x^6 + 32*x^7 - 32*x^8 + 8*x^9 -
2) + exp(x)*(16*x^4*exp(10) - exp(5)*(64*x^4 - 32*x^5) + 64*x^4 - 64*x^5 + 16*x^6) + exp(5*x)*(exp(10)*(x^2 +
2*x^5 + x^8) - exp(5)*(4*x^2 - 2*x^3 + 8*x^5 - 4*x^6 + 4*x^8 - 2*x^9) + 4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 +
2*x^7 + 4*x^8 - 4*x^9 + x^10))/(16*x^4*exp(10) - exp(5)*(64*x^4 - 32*x^5) - exp(x)*(32*x^5*exp(10) - exp(5)*(
128*x^5 - 64*x^6) + 128*x^5 - 128*x^6 + 32*x^7) + exp(4*x)*(exp(10)*(x^2 + 2*x^5 + x^8) - exp(5)*(4*x^2 - 2*x^
3 + 8*x^5 - 4*x^6 + 4*x^8 - 2*x^9) + 4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*x^7 + 4*x^8 - 4*x^9 + x^10) - exp
(3*x)*(exp(10)*(8*x^4 + 8*x^7) + 32*x^4 - 32*x^5 + 8*x^6 + 32*x^7 - 32*x^8 + 8*x^9 - exp(5)*(32*x^4 - 16*x^5 +
32*x^7 - 16*x^8)) + exp(2*x)*(exp(10)*(8*x^3 + 24*x^6) + 32*x^3 - 32*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 -
exp(5)*(32*x^3 - 16*x^4 + 96*x^6 - 48*x^7)) + 64*x^4 - 64*x^5 + 16*x^6), x)

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sympy [B]  time = 5.07, size = 155, normalized size = 4.56 \begin {gather*} \frac {4 x e^{x} - 4}{4 x^{5} - 8 x^{4} + 4 x^{4} e^{5} + 4 x^{2} - 8 x + 4 x e^{5} + \left (- 4 x^{6} - 4 x^{5} e^{5} + 8 x^{5} - 4 x^{3} - 4 x^{2} e^{5} + 8 x^{2}\right ) e^{x} + \left (x^{7} - 2 x^{6} + x^{6} e^{5} + 2 x^{4} - 4 x^{3} + 2 x^{3} e^{5} + x - 2 + e^{5}\right ) e^{2 x}} + e^{x} + \frac {1}{x^{5} + x^{4} \left (-2 + e^{5}\right ) + x^{2} + x \left (-2 + e^{5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**8+2*x**5+x**2)*exp(5)**2+(2*x**9-4*x**8+4*x**6-8*x**5+2*x**3-4*x**2)*exp(5)+x**10-4*x**9+4*x**
8+2*x**7-8*x**6+8*x**5+x**4-4*x**3+4*x**2)*exp(x)**5+((-8*x**7-8*x**4)*exp(5)**2+(-16*x**8+32*x**7-16*x**5+32*
x**4-4*x**3-1)*exp(5)-8*x**9+32*x**8-32*x**7-8*x**6+32*x**5-37*x**4+8*x**3-2*x+2)*exp(x)**4+((24*x**6+8*x**3)*
exp(5)**2+(48*x**7-96*x**6+16*x**4-36*x**3+12*x**2)*exp(5)+24*x**8-96*x**7+96*x**6+8*x**5-36*x**4+56*x**3-24*x
**2)*exp(x)**3+(-32*x**5*exp(5)**2+(-64*x**6+128*x**5+8*x**2-8*x)*exp(5)-32*x**7+128*x**6-128*x**5+8*x**3-28*x
**2+16*x)*exp(x)**2+(16*x**4*exp(5)**2+(32*x**5-64*x**4)*exp(5)+16*x**6-64*x**5+64*x**4)*exp(x))/(((x**8+2*x**
5+x**2)*exp(5)**2+(2*x**9-4*x**8+4*x**6-8*x**5+2*x**3-4*x**2)*exp(5)+x**10-4*x**9+4*x**8+2*x**7-8*x**6+8*x**5+
x**4-4*x**3+4*x**2)*exp(x)**4+((-8*x**7-8*x**4)*exp(5)**2+(-16*x**8+32*x**7-16*x**5+32*x**4)*exp(5)-8*x**9+32*
x**8-32*x**7-8*x**6+32*x**5-32*x**4)*exp(x)**3+((24*x**6+8*x**3)*exp(5)**2+(48*x**7-96*x**6+16*x**4-32*x**3)*e
xp(5)+24*x**8-96*x**7+96*x**6+8*x**5-32*x**4+32*x**3)*exp(x)**2+(-32*x**5*exp(5)**2+(-64*x**6+128*x**5)*exp(5)
-32*x**7+128*x**6-128*x**5)*exp(x)+16*x**4*exp(5)**2+(32*x**5-64*x**4)*exp(5)+16*x**6-64*x**5+64*x**4),x)

[Out]

(4*x*exp(x) - 4)/(4*x**5 - 8*x**4 + 4*x**4*exp(5) + 4*x**2 - 8*x + 4*x*exp(5) + (-4*x**6 - 4*x**5*exp(5) + 8*x
**5 - 4*x**3 - 4*x**2*exp(5) + 8*x**2)*exp(x) + (x**7 - 2*x**6 + x**6*exp(5) + 2*x**4 - 4*x**3 + 2*x**3*exp(5)
+ x - 2 + exp(5))*exp(2*x)) + exp(x) + 1/(x**5 + x**4*(-2 + exp(5)) + x**2 + x*(-2 + exp(5)))

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