3.25.13 \(\int (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7)+e^{3 e^{16}} (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7)+e^{5 e^{16}} (-576 e^{17/3} x^5-28672 e^4 x^7)+e^{6 e^{16}} (24 e^{17/3} x^5+3584 e^4 x^7)+e^{4 e^{16}} (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7)+e^{2 e^{16}} (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7)) \, dx\)

Optimal. Leaf size=27 \[ e^4 \left (e^{5/3}+\left (4-e^{e^{16}}\right )^2 x^2\right )^4 \]

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Rubi [B]  time = 0.14, antiderivative size = 318, normalized size of antiderivative = 11.78, number of steps used = 9, number of rules used = 1, integrand size = 275, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.004, Rules used = {6} \begin {gather*} e^4 \left (65536-32 e^{7 e^{16}}+e^{8 e^{16}}\right ) x^8+448 e^{4+6 e^{16}} x^8-3584 e^{4+5 e^{16}} x^8+17920 e^{4+4 e^{16}} x^8-57344 e^{4+3 e^{16}} x^8+114688 e^{4+2 e^{16}} x^8-131072 e^{4+e^{16}} x^8+4 e^{\frac {17}{3}+6 e^{16}} x^6-96 e^{\frac {17}{3}+5 e^{16}} x^6+960 e^{\frac {17}{3}+4 e^{16}} x^6-5120 e^{\frac {17}{3}+3 e^{16}} x^6+15360 e^{\frac {17}{3}+2 e^{16}} x^6-24576 e^{\frac {17}{3}+e^{16}} x^6+16384 e^{17/3} x^6+6 e^{\frac {22}{3}+4 e^{16}} x^4-96 e^{\frac {22}{3}+3 e^{16}} x^4+576 e^{\frac {22}{3}+2 e^{16}} x^4-1536 e^{\frac {22}{3}+e^{16}} x^4+1536 e^{22/3} x^4+4 e^{9+2 e^{16}} x^2-32 e^{9+e^{16}} x^2+64 e^9 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[128*E^9*x + 6144*E^(22/3)*x^3 + 98304*E^(17/3)*x^5 + 524288*E^4*x^7 - 256*E^(4 + 7*E^16)*x^7 + 8*E^(4 + 8*
E^16)*x^7 + E^E^16*(-64*E^9*x - 6144*E^(22/3)*x^3 - 147456*E^(17/3)*x^5 - 1048576*E^4*x^7) + E^(3*E^16)*(-384*
E^(22/3)*x^3 - 30720*E^(17/3)*x^5 - 458752*E^4*x^7) + E^(5*E^16)*(-576*E^(17/3)*x^5 - 28672*E^4*x^7) + E^(6*E^
16)*(24*E^(17/3)*x^5 + 3584*E^4*x^7) + E^(4*E^16)*(24*E^(22/3)*x^3 + 5760*E^(17/3)*x^5 + 143360*E^4*x^7) + E^(
2*E^16)*(8*E^9*x + 2304*E^(22/3)*x^3 + 92160*E^(17/3)*x^5 + 917504*E^4*x^7),x]

[Out]

64*E^9*x^2 - 32*E^(9 + E^16)*x^2 + 4*E^(9 + 2*E^16)*x^2 + 1536*E^(22/3)*x^4 - 1536*E^(22/3 + E^16)*x^4 + 576*E
^(22/3 + 2*E^16)*x^4 - 96*E^(22/3 + 3*E^16)*x^4 + 6*E^(22/3 + 4*E^16)*x^4 + 16384*E^(17/3)*x^6 - 24576*E^(17/3
+ E^16)*x^6 + 15360*E^(17/3 + 2*E^16)*x^6 - 5120*E^(17/3 + 3*E^16)*x^6 + 960*E^(17/3 + 4*E^16)*x^6 - 96*E^(17
/3 + 5*E^16)*x^6 + 4*E^(17/3 + 6*E^16)*x^6 - 131072*E^(4 + E^16)*x^8 + 114688*E^(4 + 2*E^16)*x^8 - 57344*E^(4
+ 3*E^16)*x^8 + 17920*E^(4 + 4*E^16)*x^8 - 3584*E^(4 + 5*E^16)*x^8 + 448*E^(4 + 6*E^16)*x^8 + E^4*(65536 - 32*
E^(7*E^16) + E^(8*E^16))*x^8

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+8 e^{4+8 e^{16}} x^7+\left (524288 e^4-256 e^{4+7 e^{16}}\right ) x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx\\ &=\int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+\left (524288 e^4-256 e^{4+7 e^{16}}+8 e^{4+8 e^{16}}\right ) x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx\\ &=64 e^9 x^2+1536 e^{22/3} x^4+16384 e^{17/3} x^6+e^4 \left (65536-32 e^{7 e^{16}}+e^{8 e^{16}}\right ) x^8+e^{e^{16}} \int \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right ) \, dx+e^{2 e^{16}} \int \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right ) \, dx+e^{3 e^{16}} \int \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right ) \, dx+e^{4 e^{16}} \int \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right ) \, dx+e^{5 e^{16}} \int \left (-576 e^{17/3} x^5-28672 e^4 x^7\right ) \, dx+e^{6 e^{16}} \int \left (24 e^{17/3} x^5+3584 e^4 x^7\right ) \, dx\\ &=64 e^9 x^2-32 e^{9+e^{16}} x^2+4 e^{9+2 e^{16}} x^2+1536 e^{22/3} x^4-1536 e^{\frac {22}{3}+e^{16}} x^4+576 e^{\frac {22}{3}+2 e^{16}} x^4-96 e^{\frac {22}{3}+3 e^{16}} x^4+6 e^{\frac {22}{3}+4 e^{16}} x^4+16384 e^{17/3} x^6-24576 e^{\frac {17}{3}+e^{16}} x^6+15360 e^{\frac {17}{3}+2 e^{16}} x^6-5120 e^{\frac {17}{3}+3 e^{16}} x^6+960 e^{\frac {17}{3}+4 e^{16}} x^6-96 e^{\frac {17}{3}+5 e^{16}} x^6+4 e^{\frac {17}{3}+6 e^{16}} x^6-131072 e^{4+e^{16}} x^8+114688 e^{4+2 e^{16}} x^8-57344 e^{4+3 e^{16}} x^8+17920 e^{4+4 e^{16}} x^8-3584 e^{4+5 e^{16}} x^8+448 e^{4+6 e^{16}} x^8+e^4 \left (65536-32 e^{7 e^{16}}+e^{8 e^{16}}\right ) x^8\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.04, size = 73, normalized size = 2.70 \begin {gather*} e^4 \left (-4+e^{e^{16}}\right )^2 x^2 \left (4 e^5+6 e^{10/3} \left (-4+e^{e^{16}}\right )^2 x^2+4 e^{5/3} \left (-4+e^{e^{16}}\right )^4 x^4+\left (-4+e^{e^{16}}\right )^6 x^6\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[128*E^9*x + 6144*E^(22/3)*x^3 + 98304*E^(17/3)*x^5 + 524288*E^4*x^7 - 256*E^(4 + 7*E^16)*x^7 + 8*E^(
4 + 8*E^16)*x^7 + E^E^16*(-64*E^9*x - 6144*E^(22/3)*x^3 - 147456*E^(17/3)*x^5 - 1048576*E^4*x^7) + E^(3*E^16)*
(-384*E^(22/3)*x^3 - 30720*E^(17/3)*x^5 - 458752*E^4*x^7) + E^(5*E^16)*(-576*E^(17/3)*x^5 - 28672*E^4*x^7) + E
^(6*E^16)*(24*E^(17/3)*x^5 + 3584*E^4*x^7) + E^(4*E^16)*(24*E^(22/3)*x^3 + 5760*E^(17/3)*x^5 + 143360*E^4*x^7)
+ E^(2*E^16)*(8*E^9*x + 2304*E^(22/3)*x^3 + 92160*E^(17/3)*x^5 + 917504*E^4*x^7),x]

[Out]

E^4*(-4 + E^E^16)^2*x^2*(4*E^5 + 6*E^(10/3)*(-4 + E^E^16)^2*x^2 + 4*E^(5/3)*(-4 + E^E^16)^4*x^4 + (-4 + E^E^16
)^6*x^6)

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fricas [B]  time = 1.16, size = 221, normalized size = 8.19 \begin {gather*} 65536 \, x^{8} e^{4} + x^{8} e^{\left (8 \, e^{16} + 4\right )} - 32 \, x^{8} e^{\left (7 \, e^{16} + 4\right )} + 16384 \, x^{6} e^{\frac {17}{3}} + 1536 \, x^{4} e^{\frac {22}{3}} + 64 \, x^{2} e^{9} + 4 \, {\left (112 \, x^{8} e^{4} + x^{6} e^{\frac {17}{3}}\right )} e^{\left (6 \, e^{16}\right )} - 32 \, {\left (112 \, x^{8} e^{4} + 3 \, x^{6} e^{\frac {17}{3}}\right )} e^{\left (5 \, e^{16}\right )} + 2 \, {\left (8960 \, x^{8} e^{4} + 480 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (4 \, e^{16}\right )} - 32 \, {\left (1792 \, x^{8} e^{4} + 160 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (3 \, e^{16}\right )} + 4 \, {\left (28672 \, x^{8} e^{4} + 3840 \, x^{6} e^{\frac {17}{3}} + 144 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (2 \, e^{16}\right )} - 32 \, {\left (4096 \, x^{8} e^{4} + 768 \, x^{6} e^{\frac {17}{3}} + 48 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (e^{16}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^7*exp(1)^4*exp(exp(16))^8-256*x^7*exp(1)^4*exp(exp(16))^7+(24*x^5*exp(1)^4*exp(5/3)+3584*x^7*exp
(1)^4)*exp(exp(16))^6+(-576*x^5*exp(1)^4*exp(5/3)-28672*x^7*exp(1)^4)*exp(exp(16))^5+(24*x^3*exp(1)^4*exp(5/3)
^2+5760*x^5*exp(1)^4*exp(5/3)+143360*x^7*exp(1)^4)*exp(exp(16))^4+(-384*x^3*exp(1)^4*exp(5/3)^2-30720*x^5*exp(
1)^4*exp(5/3)-458752*x^7*exp(1)^4)*exp(exp(16))^3+(8*x*exp(1)^4*exp(5/3)^3+2304*x^3*exp(1)^4*exp(5/3)^2+92160*
x^5*exp(1)^4*exp(5/3)+917504*x^7*exp(1)^4)*exp(exp(16))^2+(-64*x*exp(1)^4*exp(5/3)^3-6144*x^3*exp(1)^4*exp(5/3
)^2-147456*x^5*exp(1)^4*exp(5/3)-1048576*x^7*exp(1)^4)*exp(exp(16))+128*x*exp(1)^4*exp(5/3)^3+6144*x^3*exp(1)^
4*exp(5/3)^2+98304*x^5*exp(1)^4*exp(5/3)+524288*x^7*exp(1)^4,x, algorithm="fricas")

[Out]

65536*x^8*e^4 + x^8*e^(8*e^16 + 4) - 32*x^8*e^(7*e^16 + 4) + 16384*x^6*e^(17/3) + 1536*x^4*e^(22/3) + 64*x^2*e
^9 + 4*(112*x^8*e^4 + x^6*e^(17/3))*e^(6*e^16) - 32*(112*x^8*e^4 + 3*x^6*e^(17/3))*e^(5*e^16) + 2*(8960*x^8*e^
4 + 480*x^6*e^(17/3) + 3*x^4*e^(22/3))*e^(4*e^16) - 32*(1792*x^8*e^4 + 160*x^6*e^(17/3) + 3*x^4*e^(22/3))*e^(3
*e^16) + 4*(28672*x^8*e^4 + 3840*x^6*e^(17/3) + 144*x^4*e^(22/3) + x^2*e^9)*e^(2*e^16) - 32*(4096*x^8*e^4 + 76
8*x^6*e^(17/3) + 48*x^4*e^(22/3) + x^2*e^9)*e^(e^16)

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giac [B]  time = 0.31, size = 221, normalized size = 8.19 \begin {gather*} 65536 \, x^{8} e^{4} + x^{8} e^{\left (8 \, e^{16} + 4\right )} - 32 \, x^{8} e^{\left (7 \, e^{16} + 4\right )} + 16384 \, x^{6} e^{\frac {17}{3}} + 1536 \, x^{4} e^{\frac {22}{3}} + 64 \, x^{2} e^{9} + 4 \, {\left (112 \, x^{8} e^{4} + x^{6} e^{\frac {17}{3}}\right )} e^{\left (6 \, e^{16}\right )} - 32 \, {\left (112 \, x^{8} e^{4} + 3 \, x^{6} e^{\frac {17}{3}}\right )} e^{\left (5 \, e^{16}\right )} + 2 \, {\left (8960 \, x^{8} e^{4} + 480 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (4 \, e^{16}\right )} - 32 \, {\left (1792 \, x^{8} e^{4} + 160 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (3 \, e^{16}\right )} + 4 \, {\left (28672 \, x^{8} e^{4} + 3840 \, x^{6} e^{\frac {17}{3}} + 144 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (2 \, e^{16}\right )} - 32 \, {\left (4096 \, x^{8} e^{4} + 768 \, x^{6} e^{\frac {17}{3}} + 48 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (e^{16}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^7*exp(1)^4*exp(exp(16))^8-256*x^7*exp(1)^4*exp(exp(16))^7+(24*x^5*exp(1)^4*exp(5/3)+3584*x^7*exp
(1)^4)*exp(exp(16))^6+(-576*x^5*exp(1)^4*exp(5/3)-28672*x^7*exp(1)^4)*exp(exp(16))^5+(24*x^3*exp(1)^4*exp(5/3)
^2+5760*x^5*exp(1)^4*exp(5/3)+143360*x^7*exp(1)^4)*exp(exp(16))^4+(-384*x^3*exp(1)^4*exp(5/3)^2-30720*x^5*exp(
1)^4*exp(5/3)-458752*x^7*exp(1)^4)*exp(exp(16))^3+(8*x*exp(1)^4*exp(5/3)^3+2304*x^3*exp(1)^4*exp(5/3)^2+92160*
x^5*exp(1)^4*exp(5/3)+917504*x^7*exp(1)^4)*exp(exp(16))^2+(-64*x*exp(1)^4*exp(5/3)^3-6144*x^3*exp(1)^4*exp(5/3
)^2-147456*x^5*exp(1)^4*exp(5/3)-1048576*x^7*exp(1)^4)*exp(exp(16))+128*x*exp(1)^4*exp(5/3)^3+6144*x^3*exp(1)^
4*exp(5/3)^2+98304*x^5*exp(1)^4*exp(5/3)+524288*x^7*exp(1)^4,x, algorithm="giac")

[Out]

65536*x^8*e^4 + x^8*e^(8*e^16 + 4) - 32*x^8*e^(7*e^16 + 4) + 16384*x^6*e^(17/3) + 1536*x^4*e^(22/3) + 64*x^2*e
^9 + 4*(112*x^8*e^4 + x^6*e^(17/3))*e^(6*e^16) - 32*(112*x^8*e^4 + 3*x^6*e^(17/3))*e^(5*e^16) + 2*(8960*x^8*e^
4 + 480*x^6*e^(17/3) + 3*x^4*e^(22/3))*e^(4*e^16) - 32*(1792*x^8*e^4 + 160*x^6*e^(17/3) + 3*x^4*e^(22/3))*e^(3
*e^16) + 4*(28672*x^8*e^4 + 3840*x^6*e^(17/3) + 144*x^4*e^(22/3) + x^2*e^9)*e^(2*e^16) - 32*(4096*x^8*e^4 + 76
8*x^6*e^(17/3) + 48*x^4*e^(22/3) + x^2*e^9)*e^(e^16)

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maple [B]  time = 0.15, size = 178, normalized size = 6.59

method	result	size
gosper	\(\left ({\mathrm e}^{2 \,{\mathrm e}^{16}}-8 \,{\mathrm e}^{{\mathrm e}^{16}}+16\right ) {\mathrm e}^{4} \left ({\mathrm e}^{6 \,{\mathrm e}^{16}} x^{6}-24 \,{\mathrm e}^{5 \,{\mathrm e}^{16}} x^{6}+240 \,{\mathrm e}^{4 \,{\mathrm e}^{16}} x^{6}+4 \,{\mathrm e}^{\frac {5}{3}} {\mathrm e}^{4 \,{\mathrm e}^{16}} x^{4}-1280 \,{\mathrm e}^{3 \,{\mathrm e}^{16}} x^{6}-64 \,{\mathrm e}^{\frac {5}{3}} {\mathrm e}^{3 \,{\mathrm e}^{16}} x^{4}+3840 \,{\mathrm e}^{2 \,{\mathrm e}^{16}} x^{6}+384 \,{\mathrm e}^{\frac {5}{3}} {\mathrm e}^{2 \,{\mathrm e}^{16}} x^{4}-6144 \,{\mathrm e}^{{\mathrm e}^{16}} x^{6}+6 \,{\mathrm e}^{\frac {10}{3}} {\mathrm e}^{2 \,{\mathrm e}^{16}} x^{2}-1024 \,{\mathrm e}^{\frac {5}{3}} {\mathrm e}^{{\mathrm e}^{16}} x^{4}+4096 x^{6}-48 \,{\mathrm e}^{\frac {10}{3}} {\mathrm e}^{{\mathrm e}^{16}} x^{2}+1024 \,{\mathrm e}^{\frac {5}{3}} x^{4}+96 \,{\mathrm e}^{\frac {10}{3}} x^{2}+4 \,{\mathrm e}^{5}\right ) x^{2}\)	\(178\)
risch	\(x^{8} {\mathrm e}^{4+8 \,{\mathrm e}^{16}}-32 x^{8} {\mathrm e}^{4+7 \,{\mathrm e}^{16}}+448 \,{\mathrm e}^{6 \,{\mathrm e}^{16}+4} x^{8}+4 \,{\mathrm e}^{6 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}-3584 \,{\mathrm e}^{5 \,{\mathrm e}^{16}+4} x^{8}-96 \,{\mathrm e}^{5 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}+17920 \,{\mathrm e}^{4 \,{\mathrm e}^{16}+4} x^{8}+960 \,{\mathrm e}^{4 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}+6 \,{\mathrm e}^{4 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {10}{3}} x^{4}-57344 \,{\mathrm e}^{3 \,{\mathrm e}^{16}+4} x^{8}-5120 \,{\mathrm e}^{3 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}-96 \,{\mathrm e}^{3 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {10}{3}} x^{4}+114688 \,{\mathrm e}^{2 \,{\mathrm e}^{16}+4} x^{8}+15360 \,{\mathrm e}^{2 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}+576 \,{\mathrm e}^{2 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {10}{3}} x^{4}+4 \,{\mathrm e}^{2 \,{\mathrm e}^{16}+4} {\mathrm e}^{5} x^{2}-131072 \,{\mathrm e}^{{\mathrm e}^{16}+4} x^{8}-24576 \,{\mathrm e}^{{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}-1536 \,{\mathrm e}^{{\mathrm e}^{16}+4} {\mathrm e}^{\frac {10}{3}} x^{4}-32 \,{\mathrm e}^{{\mathrm e}^{16}+4} {\mathrm e}^{5} x^{2}+64 x^{2} {\mathrm e}^{9}+1536 \,{\mathrm e}^{\frac {22}{3}} x^{4}+16384 \,{\mathrm e}^{\frac {17}{3}} x^{6}+65536 x^{8} {\mathrm e}^{4}\)	\(285\)
norman	\(\left (4 \,{\mathrm e}^{4} {\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{16}}-32 \,{\mathrm e}^{4} {\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{16}}+64 \,{\mathrm e}^{4} {\mathrm e}^{5}\right ) x^{2}+\left (6 \,{\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}} {\mathrm e}^{4 \,{\mathrm e}^{16}}-96 \,{\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}} {\mathrm e}^{3 \,{\mathrm e}^{16}}+576 \,{\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}} {\mathrm e}^{2 \,{\mathrm e}^{16}}-1536 \,{\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}} {\mathrm e}^{{\mathrm e}^{16}}+1536 \,{\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}}\right ) x^{4}+\left (4 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}} {\mathrm e}^{6 \,{\mathrm e}^{16}}-96 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}} {\mathrm e}^{5 \,{\mathrm e}^{16}}+960 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}} {\mathrm e}^{4 \,{\mathrm e}^{16}}-5120 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}} {\mathrm e}^{3 \,{\mathrm e}^{16}}+15360 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}} {\mathrm e}^{2 \,{\mathrm e}^{16}}-24576 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}} {\mathrm e}^{{\mathrm e}^{16}}+16384 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}\right ) x^{6}+\left ({\mathrm e}^{4} {\mathrm e}^{8 \,{\mathrm e}^{16}}-32 \,{\mathrm e}^{4} {\mathrm e}^{7 \,{\mathrm e}^{16}}+448 \,{\mathrm e}^{4} {\mathrm e}^{6 \,{\mathrm e}^{16}}-3584 \,{\mathrm e}^{4} {\mathrm e}^{5 \,{\mathrm e}^{16}}+17920 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}}-57344 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}}+114688 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}}-131072 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}}+65536 \,{\mathrm e}^{4}\right ) x^{8}\)	\(303\)
default	\({\mathrm e}^{4} {\mathrm e}^{8 \,{\mathrm e}^{16}} x^{8}-32 \,{\mathrm e}^{4} {\mathrm e}^{7 \,{\mathrm e}^{16}} x^{8}+{\mathrm e}^{6 \,{\mathrm e}^{16}} \left (4 x^{6} {\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}+448 x^{8} {\mathrm e}^{4}\right )+{\mathrm e}^{5 \,{\mathrm e}^{16}} \left (-96 x^{6} {\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}-3584 x^{8} {\mathrm e}^{4}\right )+{\mathrm e}^{4 \,{\mathrm e}^{16}} \left (6 x^{4} {\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}}+960 x^{6} {\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}+17920 x^{8} {\mathrm e}^{4}\right )+{\mathrm e}^{3 \,{\mathrm e}^{16}} \left (-96 x^{4} {\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}}-5120 x^{6} {\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}-57344 x^{8} {\mathrm e}^{4}\right )+{\mathrm e}^{2 \,{\mathrm e}^{16}} \left (4 x^{2} {\mathrm e}^{4} {\mathrm e}^{5}+576 x^{4} {\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}}+15360 x^{6} {\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}+114688 x^{8} {\mathrm e}^{4}\right )+{\mathrm e}^{{\mathrm e}^{16}} \left (-32 x^{2} {\mathrm e}^{4} {\mathrm e}^{5}-1536 x^{4} {\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}}-24576 x^{6} {\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}-131072 x^{8} {\mathrm e}^{4}\right )+64 x^{2} {\mathrm e}^{4} {\mathrm e}^{5}+1536 x^{4} {\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}}+16384 x^{6} {\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}+65536 x^{8} {\mathrm e}^{4}\)	\(313\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*x^7*exp(1)^4*exp(exp(16))^8-256*x^7*exp(1)^4*exp(exp(16))^7+(24*x^5*exp(1)^4*exp(5/3)+3584*x^7*exp(1)^4)
*exp(exp(16))^6+(-576*x^5*exp(1)^4*exp(5/3)-28672*x^7*exp(1)^4)*exp(exp(16))^5+(24*x^3*exp(1)^4*exp(5/3)^2+576
0*x^5*exp(1)^4*exp(5/3)+143360*x^7*exp(1)^4)*exp(exp(16))^4+(-384*x^3*exp(1)^4*exp(5/3)^2-30720*x^5*exp(1)^4*e
xp(5/3)-458752*x^7*exp(1)^4)*exp(exp(16))^3+(8*x*exp(1)^4*exp(5/3)^3+2304*x^3*exp(1)^4*exp(5/3)^2+92160*x^5*ex
p(1)^4*exp(5/3)+917504*x^7*exp(1)^4)*exp(exp(16))^2+(-64*x*exp(1)^4*exp(5/3)^3-6144*x^3*exp(1)^4*exp(5/3)^2-14
7456*x^5*exp(1)^4*exp(5/3)-1048576*x^7*exp(1)^4)*exp(exp(16))+128*x*exp(1)^4*exp(5/3)^3+6144*x^3*exp(1)^4*exp(
5/3)^2+98304*x^5*exp(1)^4*exp(5/3)+524288*x^7*exp(1)^4,x,method=_RETURNVERBOSE)

[Out]

(exp(exp(16))^2-8*exp(exp(16))+16)*exp(1)^4*(exp(exp(16))^6*x^6-24*exp(exp(16))^5*x^6+240*exp(exp(16))^4*x^6+4
*exp(5/3)*exp(exp(16))^4*x^4-1280*exp(exp(16))^3*x^6-64*exp(5/3)*exp(exp(16))^3*x^4+3840*exp(exp(16))^2*x^6+38
4*exp(5/3)*exp(exp(16))^2*x^4-6144*exp(exp(16))*x^6+6*exp(5/3)^2*exp(exp(16))^2*x^2-1024*exp(5/3)*exp(exp(16))
*x^4+4096*x^6-48*exp(5/3)^2*exp(exp(16))*x^2+1024*exp(5/3)*x^4+96*exp(5/3)^2*x^2+4*exp(5/3)^3)*x^2

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maxima [B]  time = 0.46, size = 221, normalized size = 8.19 \begin {gather*} 65536 \, x^{8} e^{4} + x^{8} e^{\left (8 \, e^{16} + 4\right )} - 32 \, x^{8} e^{\left (7 \, e^{16} + 4\right )} + 16384 \, x^{6} e^{\frac {17}{3}} + 1536 \, x^{4} e^{\frac {22}{3}} + 64 \, x^{2} e^{9} + 4 \, {\left (112 \, x^{8} e^{4} + x^{6} e^{\frac {17}{3}}\right )} e^{\left (6 \, e^{16}\right )} - 32 \, {\left (112 \, x^{8} e^{4} + 3 \, x^{6} e^{\frac {17}{3}}\right )} e^{\left (5 \, e^{16}\right )} + 2 \, {\left (8960 \, x^{8} e^{4} + 480 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (4 \, e^{16}\right )} - 32 \, {\left (1792 \, x^{8} e^{4} + 160 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (3 \, e^{16}\right )} + 4 \, {\left (28672 \, x^{8} e^{4} + 3840 \, x^{6} e^{\frac {17}{3}} + 144 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (2 \, e^{16}\right )} - 32 \, {\left (4096 \, x^{8} e^{4} + 768 \, x^{6} e^{\frac {17}{3}} + 48 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (e^{16}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^7*exp(1)^4*exp(exp(16))^8-256*x^7*exp(1)^4*exp(exp(16))^7+(24*x^5*exp(1)^4*exp(5/3)+3584*x^7*exp
(1)^4)*exp(exp(16))^6+(-576*x^5*exp(1)^4*exp(5/3)-28672*x^7*exp(1)^4)*exp(exp(16))^5+(24*x^3*exp(1)^4*exp(5/3)
^2+5760*x^5*exp(1)^4*exp(5/3)+143360*x^7*exp(1)^4)*exp(exp(16))^4+(-384*x^3*exp(1)^4*exp(5/3)^2-30720*x^5*exp(
1)^4*exp(5/3)-458752*x^7*exp(1)^4)*exp(exp(16))^3+(8*x*exp(1)^4*exp(5/3)^3+2304*x^3*exp(1)^4*exp(5/3)^2+92160*
x^5*exp(1)^4*exp(5/3)+917504*x^7*exp(1)^4)*exp(exp(16))^2+(-64*x*exp(1)^4*exp(5/3)^3-6144*x^3*exp(1)^4*exp(5/3
)^2-147456*x^5*exp(1)^4*exp(5/3)-1048576*x^7*exp(1)^4)*exp(exp(16))+128*x*exp(1)^4*exp(5/3)^3+6144*x^3*exp(1)^
4*exp(5/3)^2+98304*x^5*exp(1)^4*exp(5/3)+524288*x^7*exp(1)^4,x, algorithm="maxima")

[Out]

65536*x^8*e^4 + x^8*e^(8*e^16 + 4) - 32*x^8*e^(7*e^16 + 4) + 16384*x^6*e^(17/3) + 1536*x^4*e^(22/3) + 64*x^2*e
^9 + 4*(112*x^8*e^4 + x^6*e^(17/3))*e^(6*e^16) - 32*(112*x^8*e^4 + 3*x^6*e^(17/3))*e^(5*e^16) + 2*(8960*x^8*e^
4 + 480*x^6*e^(17/3) + 3*x^4*e^(22/3))*e^(4*e^16) - 32*(1792*x^8*e^4 + 160*x^6*e^(17/3) + 3*x^4*e^(22/3))*e^(3
*e^16) + 4*(28672*x^8*e^4 + 3840*x^6*e^(17/3) + 144*x^4*e^(22/3) + x^2*e^9)*e^(2*e^16) - 32*(4096*x^8*e^4 + 76
8*x^6*e^(17/3) + 48*x^4*e^(22/3) + x^2*e^9)*e^(e^16)

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mupad [B]  time = 1.68, size = 207, normalized size = 7.67 \begin {gather*} \left (65536\,{\mathrm {e}}^4-131072\,{\mathrm {e}}^{{\mathrm {e}}^{16}+4}+114688\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}+4}-57344\,{\mathrm {e}}^{3\,{\mathrm {e}}^{16}+4}+17920\,{\mathrm {e}}^{4\,{\mathrm {e}}^{16}+4}-3584\,{\mathrm {e}}^{5\,{\mathrm {e}}^{16}+4}+448\,{\mathrm {e}}^{6\,{\mathrm {e}}^{16}+4}-32\,{\mathrm {e}}^{7\,{\mathrm {e}}^{16}+4}+{\mathrm {e}}^{8\,{\mathrm {e}}^{16}+4}\right )\,x^8+\left (16384\,{\mathrm {e}}^{17/3}-24576\,{\mathrm {e}}^{{\mathrm {e}}^{16}+\frac {17}{3}}+15360\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}+\frac {17}{3}}-5120\,{\mathrm {e}}^{3\,{\mathrm {e}}^{16}+\frac {17}{3}}+960\,{\mathrm {e}}^{4\,{\mathrm {e}}^{16}+\frac {17}{3}}-96\,{\mathrm {e}}^{5\,{\mathrm {e}}^{16}+\frac {17}{3}}+4\,{\mathrm {e}}^{6\,{\mathrm {e}}^{16}+\frac {17}{3}}\right )\,x^6+\left (1536\,{\mathrm {e}}^{22/3}-1536\,{\mathrm {e}}^{{\mathrm {e}}^{16}+\frac {22}{3}}+576\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}+\frac {22}{3}}-96\,{\mathrm {e}}^{3\,{\mathrm {e}}^{16}+\frac {22}{3}}+6\,{\mathrm {e}}^{4\,{\mathrm {e}}^{16}+\frac {22}{3}}\right )\,x^4+\left (64\,{\mathrm {e}}^9-32\,{\mathrm {e}}^{{\mathrm {e}}^{16}+9}+4\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}+9}\right )\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(6*exp(16))*(3584*x^7*exp(4) + 24*x^5*exp(17/3)) - exp(5*exp(16))*(28672*x^7*exp(4) + 576*x^5*exp(17/3)
) + 128*x*exp(9) - exp(exp(16))*(64*x*exp(9) + 1048576*x^7*exp(4) + 147456*x^5*exp(17/3) + 6144*x^3*exp(22/3))
+ 524288*x^7*exp(4) + 98304*x^5*exp(17/3) + 6144*x^3*exp(22/3) + exp(4*exp(16))*(143360*x^7*exp(4) + 5760*x^5
*exp(17/3) + 24*x^3*exp(22/3)) - exp(3*exp(16))*(458752*x^7*exp(4) + 30720*x^5*exp(17/3) + 384*x^3*exp(22/3))
+ exp(2*exp(16))*(8*x*exp(9) + 917504*x^7*exp(4) + 92160*x^5*exp(17/3) + 2304*x^3*exp(22/3)) - 256*x^7*exp(7*e
xp(16))*exp(4) + 8*x^7*exp(8*exp(16))*exp(4),x)

[Out]

x^6*(16384*exp(17/3) - 24576*exp(exp(16) + 17/3) + 15360*exp(2*exp(16) + 17/3) - 5120*exp(3*exp(16) + 17/3) +
960*exp(4*exp(16) + 17/3) - 96*exp(5*exp(16) + 17/3) + 4*exp(6*exp(16) + 17/3)) + x^4*(1536*exp(22/3) - 1536*e
xp(exp(16) + 22/3) + 576*exp(2*exp(16) + 22/3) - 96*exp(3*exp(16) + 22/3) + 6*exp(4*exp(16) + 22/3)) + x^2*(64
*exp(9) - 32*exp(exp(16) + 9) + 4*exp(2*exp(16) + 9)) + x^8*(65536*exp(4) - 131072*exp(exp(16) + 4) + 114688*e
xp(2*exp(16) + 4) - 57344*exp(3*exp(16) + 4) + 17920*exp(4*exp(16) + 4) - 3584*exp(5*exp(16) + 4) + 448*exp(6*
exp(16) + 4) - 32*exp(7*exp(16) + 4) + exp(8*exp(16) + 4))

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sympy [B]  time = 0.16, size = 282, normalized size = 10.44 \begin {gather*} x^{8} \left (65536 e^{4} + e^{4} e^{8 e^{16}} - 131072 e^{4} e^{e^{16}} - 57344 e^{4} e^{3 e^{16}} - 3584 e^{4} e^{5 e^{16}} - 32 e^{4} e^{7 e^{16}} + 448 e^{4} e^{6 e^{16}} + 17920 e^{4} e^{4 e^{16}} + 114688 e^{4} e^{2 e^{16}}\right ) + x^{6} \left (16384 e^{\frac {17}{3}} - 24576 e^{\frac {17}{3}} e^{e^{16}} - 5120 e^{\frac {17}{3}} e^{3 e^{16}} - 96 e^{\frac {17}{3}} e^{5 e^{16}} + 4 e^{\frac {17}{3}} e^{6 e^{16}} + 960 e^{\frac {17}{3}} e^{4 e^{16}} + 15360 e^{\frac {17}{3}} e^{2 e^{16}}\right ) + x^{4} \left (1536 e^{\frac {22}{3}} - 1536 e^{\frac {22}{3}} e^{e^{16}} - 96 e^{\frac {22}{3}} e^{3 e^{16}} + 6 e^{\frac {22}{3}} e^{4 e^{16}} + 576 e^{\frac {22}{3}} e^{2 e^{16}}\right ) + x^{2} \left (64 e^{9} - 32 e^{9} e^{e^{16}} + 4 e^{9} e^{2 e^{16}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x**7*exp(1)**4*exp(exp(16))**8-256*x**7*exp(1)**4*exp(exp(16))**7+(24*x**5*exp(1)**4*exp(5/3)+3584
*x**7*exp(1)**4)*exp(exp(16))**6+(-576*x**5*exp(1)**4*exp(5/3)-28672*x**7*exp(1)**4)*exp(exp(16))**5+(24*x**3*
exp(1)**4*exp(5/3)**2+5760*x**5*exp(1)**4*exp(5/3)+143360*x**7*exp(1)**4)*exp(exp(16))**4+(-384*x**3*exp(1)**4
*exp(5/3)**2-30720*x**5*exp(1)**4*exp(5/3)-458752*x**7*exp(1)**4)*exp(exp(16))**3+(8*x*exp(1)**4*exp(5/3)**3+2
304*x**3*exp(1)**4*exp(5/3)**2+92160*x**5*exp(1)**4*exp(5/3)+917504*x**7*exp(1)**4)*exp(exp(16))**2+(-64*x*exp
(1)**4*exp(5/3)**3-6144*x**3*exp(1)**4*exp(5/3)**2-147456*x**5*exp(1)**4*exp(5/3)-1048576*x**7*exp(1)**4)*exp(
exp(16))+128*x*exp(1)**4*exp(5/3)**3+6144*x**3*exp(1)**4*exp(5/3)**2+98304*x**5*exp(1)**4*exp(5/3)+524288*x**7
*exp(1)**4,x)

[Out]

x**8*(65536*exp(4) + exp(4)*exp(8*exp(16)) - 131072*exp(4)*exp(exp(16)) - 57344*exp(4)*exp(3*exp(16)) - 3584*e
xp(4)*exp(5*exp(16)) - 32*exp(4)*exp(7*exp(16)) + 448*exp(4)*exp(6*exp(16)) + 17920*exp(4)*exp(4*exp(16)) + 11
4688*exp(4)*exp(2*exp(16))) + x**6*(16384*exp(17/3) - 24576*exp(17/3)*exp(exp(16)) - 5120*exp(17/3)*exp(3*exp(
16)) - 96*exp(17/3)*exp(5*exp(16)) + 4*exp(17/3)*exp(6*exp(16)) + 960*exp(17/3)*exp(4*exp(16)) + 15360*exp(17/
3)*exp(2*exp(16))) + x**4*(1536*exp(22/3) - 1536*exp(22/3)*exp(exp(16)) - 96*exp(22/3)*exp(3*exp(16)) + 6*exp(
22/3)*exp(4*exp(16)) + 576*exp(22/3)*exp(2*exp(16))) + x**2*(64*exp(9) - 32*exp(9)*exp(exp(16)) + 4*exp(9)*exp
(2*exp(16)))

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