3.71.74 \(\int (18 x+e^{25} (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} (-48 x-72 x^2-24 x^3)+e^5 (-144 x^2-192 x^3-60 x^4))+e^{50} (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} (32 x+96 x^2+96 x^3+40 x^4+6 x^5)+e^{15} (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6)+e^{10} (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7)+e^5 (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8))) \, dx\)

Optimal. Leaf size=28 \[ x^2 \left (3+e^{25} (2+x)^2 \left (6-\left (e^5+x\right )^2\right )\right )^2 \]

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Rubi [B]  time = 0.15, antiderivative size = 356, normalized size of antiderivative = 12.71, number of steps used = 9, number of rules used = 0, integrand size = 254, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} e^{50} x^{10}+4 e^{55} x^9+8 e^{50} x^9+6 e^{60} x^8+32 e^{55} x^8+12 e^{50} x^8+4 e^{65} x^7+48 e^{60} x^7+72 e^{55} x^7-64 e^{50} x^7+e^{70} x^6+32 e^{65} x^6+132 e^{60} x^6-64 e^{55} x^6-236 e^{50} x^6-6 e^{25} x^6+8 e^{70} x^5+96 e^{65} x^5+96 e^{60} x^5-512 e^{55} x^5-96 e^{50} x^5-12 e^{30} x^5-24 e^{25} x^5+24 e^{70} x^4+128 e^{65} x^4-192 e^{60} x^4-768 e^{55} x^4+672 e^{50} x^4-6 e^{35} x^4-48 e^{30} x^4+12 e^{25} x^4+32 e^{70} x^3+64 e^{65} x^3-384 e^{60} x^3-384 e^{55} x^3+1152 e^{50} x^3-24 e^{35} x^3-48 e^{30} x^3+144 e^{25} x^3+16 e^{70} x^2-192 e^{60} x^2+576 e^{50} x^2-24 e^{35} x^2+144 e^{25} x^2+9 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[18*x + E^25*(288*x + 432*x^2 + 48*x^3 - 120*x^4 - 36*x^5 + E^10*(-48*x - 72*x^2 - 24*x^3) + E^5*(-144*x^2
- 192*x^3 - 60*x^4)) + E^50*(1152*x + 3456*x^2 + 2688*x^3 - 480*x^4 - 1416*x^5 - 448*x^6 + 96*x^7 + 72*x^8 + 1
0*x^9 + E^20*(32*x + 96*x^2 + 96*x^3 + 40*x^4 + 6*x^5) + E^15*(192*x^2 + 512*x^3 + 480*x^4 + 192*x^5 + 28*x^6)
+ E^10*(-384*x - 1152*x^2 - 768*x^3 + 480*x^4 + 792*x^5 + 336*x^6 + 48*x^7) + E^5*(-1152*x^2 - 3072*x^3 - 256
0*x^4 - 384*x^5 + 504*x^6 + 256*x^7 + 36*x^8)),x]

[Out]

9*x^2 + 144*E^25*x^2 - 24*E^35*x^2 + 576*E^50*x^2 - 192*E^60*x^2 + 16*E^70*x^2 + 144*E^25*x^3 - 48*E^30*x^3 -
24*E^35*x^3 + 1152*E^50*x^3 - 384*E^55*x^3 - 384*E^60*x^3 + 64*E^65*x^3 + 32*E^70*x^3 + 12*E^25*x^4 - 48*E^30*
x^4 - 6*E^35*x^4 + 672*E^50*x^4 - 768*E^55*x^4 - 192*E^60*x^4 + 128*E^65*x^4 + 24*E^70*x^4 - 24*E^25*x^5 - 12*
E^30*x^5 - 96*E^50*x^5 - 512*E^55*x^5 + 96*E^60*x^5 + 96*E^65*x^5 + 8*E^70*x^5 - 6*E^25*x^6 - 236*E^50*x^6 - 6
4*E^55*x^6 + 132*E^60*x^6 + 32*E^65*x^6 + E^70*x^6 - 64*E^50*x^7 + 72*E^55*x^7 + 48*E^60*x^7 + 4*E^65*x^7 + 12
*E^50*x^8 + 32*E^55*x^8 + 6*E^60*x^8 + 8*E^50*x^9 + 4*E^55*x^9 + E^50*x^10

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=9 x^2+e^{25} \int \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right ) \, dx+e^{50} \int \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right ) \, dx\\ &=9 x^2+144 e^{25} x^2+576 e^{50} x^2+144 e^{25} x^3+1152 e^{50} x^3+12 e^{25} x^4+672 e^{50} x^4-24 e^{25} x^5-96 e^{50} x^5-6 e^{25} x^6-236 e^{50} x^6-64 e^{50} x^7+12 e^{50} x^8+8 e^{50} x^9+e^{50} x^{10}+e^{30} \int \left (-144 x^2-192 x^3-60 x^4\right ) \, dx+e^{35} \int \left (-48 x-72 x^2-24 x^3\right ) \, dx+e^{55} \int \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right ) \, dx+e^{60} \int \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right ) \, dx+e^{65} \int \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right ) \, dx+e^{70} \int \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right ) \, dx\\ &=9 x^2+144 e^{25} x^2-24 e^{35} x^2+576 e^{50} x^2-192 e^{60} x^2+16 e^{70} x^2+144 e^{25} x^3-48 e^{30} x^3-24 e^{35} x^3+1152 e^{50} x^3-384 e^{55} x^3-384 e^{60} x^3+64 e^{65} x^3+32 e^{70} x^3+12 e^{25} x^4-48 e^{30} x^4-6 e^{35} x^4+672 e^{50} x^4-768 e^{55} x^4-192 e^{60} x^4+128 e^{65} x^4+24 e^{70} x^4-24 e^{25} x^5-12 e^{30} x^5-96 e^{50} x^5-512 e^{55} x^5+96 e^{60} x^5+96 e^{65} x^5+8 e^{70} x^5-6 e^{25} x^6-236 e^{50} x^6-64 e^{55} x^6+132 e^{60} x^6+32 e^{65} x^6+e^{70} x^6-64 e^{50} x^7+72 e^{55} x^7+48 e^{60} x^7+4 e^{65} x^7+12 e^{50} x^8+32 e^{55} x^8+6 e^{60} x^8+8 e^{50} x^9+4 e^{55} x^9+e^{50} x^{10}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.06, size = 42, normalized size = 1.50 \begin {gather*} x^2 \left (-3+e^{35} (2+x)^2+2 e^{30} x (2+x)^2+e^{25} (2+x)^2 \left (-6+x^2\right )\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[18*x + E^25*(288*x + 432*x^2 + 48*x^3 - 120*x^4 - 36*x^5 + E^10*(-48*x - 72*x^2 - 24*x^3) + E^5*(-14
4*x^2 - 192*x^3 - 60*x^4)) + E^50*(1152*x + 3456*x^2 + 2688*x^3 - 480*x^4 - 1416*x^5 - 448*x^6 + 96*x^7 + 72*x
^8 + 10*x^9 + E^20*(32*x + 96*x^2 + 96*x^3 + 40*x^4 + 6*x^5) + E^15*(192*x^2 + 512*x^3 + 480*x^4 + 192*x^5 + 2
8*x^6) + E^10*(-384*x - 1152*x^2 - 768*x^3 + 480*x^4 + 792*x^5 + 336*x^6 + 48*x^7) + E^5*(-1152*x^2 - 3072*x^3
- 2560*x^4 - 384*x^5 + 504*x^6 + 256*x^7 + 36*x^8)),x]

[Out]

x^2*(-3 + E^35*(2 + x)^2 + 2*E^30*x*(2 + x)^2 + E^25*(2 + x)^2*(-6 + x^2))^2

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fricas [B]  time = 0.70, size = 248, normalized size = 8.86 \begin {gather*} 9 \, x^{2} + {\left (x^{6} + 8 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 16 \, x^{2}\right )} e^{70} + 4 \, {\left (x^{7} + 8 \, x^{6} + 24 \, x^{5} + 32 \, x^{4} + 16 \, x^{3}\right )} e^{65} + 6 \, {\left (x^{8} + 8 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 32 \, x^{4} - 64 \, x^{3} - 32 \, x^{2}\right )} e^{60} + 4 \, {\left (x^{9} + 8 \, x^{8} + 18 \, x^{7} - 16 \, x^{6} - 128 \, x^{5} - 192 \, x^{4} - 96 \, x^{3}\right )} e^{55} + {\left (x^{10} + 8 \, x^{9} + 12 \, x^{8} - 64 \, x^{7} - 236 \, x^{6} - 96 \, x^{5} + 672 \, x^{4} + 1152 \, x^{3} + 576 \, x^{2}\right )} e^{50} - 6 \, {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{35} - 12 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} e^{30} - 6 \, {\left (x^{6} + 4 \, x^{5} - 2 \, x^{4} - 24 \, x^{3} - 24 \, x^{2}\right )} e^{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480*x^4+512*x^3+192*x^2)*exp(5)^3+(48*x^
7+336*x^6+792*x^5+480*x^4-768*x^3-1152*x^2-384*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-1
152*x^2)*exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456*x^2+1152*x)*exp(25)^2+((-24*x^3-72
*x^2-48*x)*exp(5)^2+(-60*x^4-192*x^3-144*x^2)*exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x, algo
rithm="fricas")

[Out]

9*x^2 + (x^6 + 8*x^5 + 24*x^4 + 32*x^3 + 16*x^2)*e^70 + 4*(x^7 + 8*x^6 + 24*x^5 + 32*x^4 + 16*x^3)*e^65 + 6*(x
^8 + 8*x^7 + 22*x^6 + 16*x^5 - 32*x^4 - 64*x^3 - 32*x^2)*e^60 + 4*(x^9 + 8*x^8 + 18*x^7 - 16*x^6 - 128*x^5 - 1
92*x^4 - 96*x^3)*e^55 + (x^10 + 8*x^9 + 12*x^8 - 64*x^7 - 236*x^6 - 96*x^5 + 672*x^4 + 1152*x^3 + 576*x^2)*e^5
0 - 6*(x^4 + 4*x^3 + 4*x^2)*e^35 - 12*(x^5 + 4*x^4 + 4*x^3)*e^30 - 6*(x^6 + 4*x^5 - 2*x^4 - 24*x^3 - 24*x^2)*e
^25

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giac [B]  time = 0.14, size = 247, normalized size = 8.82 \begin {gather*} 9 \, x^{2} + {\left (x^{10} + 8 \, x^{9} + 12 \, x^{8} - 64 \, x^{7} - 236 \, x^{6} - 96 \, x^{5} + 672 \, x^{4} + 1152 \, x^{3} + 576 \, x^{2} + {\left (x^{6} + 8 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 16 \, x^{2}\right )} e^{20} + 4 \, {\left (x^{7} + 8 \, x^{6} + 24 \, x^{5} + 32 \, x^{4} + 16 \, x^{3}\right )} e^{15} + 6 \, {\left (x^{8} + 8 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 32 \, x^{4} - 64 \, x^{3} - 32 \, x^{2}\right )} e^{10} + 4 \, {\left (x^{9} + 8 \, x^{8} + 18 \, x^{7} - 16 \, x^{6} - 128 \, x^{5} - 192 \, x^{4} - 96 \, x^{3}\right )} e^{5}\right )} e^{50} - 6 \, {\left (x^{6} + 4 \, x^{5} - 2 \, x^{4} - 24 \, x^{3} - 24 \, x^{2} + {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{10} + 2 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} e^{5}\right )} e^{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480*x^4+512*x^3+192*x^2)*exp(5)^3+(48*x^
7+336*x^6+792*x^5+480*x^4-768*x^3-1152*x^2-384*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-1
152*x^2)*exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456*x^2+1152*x)*exp(25)^2+((-24*x^3-72
*x^2-48*x)*exp(5)^2+(-60*x^4-192*x^3-144*x^2)*exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x, algo
rithm="giac")

[Out]

9*x^2 + (x^10 + 8*x^9 + 12*x^8 - 64*x^7 - 236*x^6 - 96*x^5 + 672*x^4 + 1152*x^3 + 576*x^2 + (x^6 + 8*x^5 + 24*
x^4 + 32*x^3 + 16*x^2)*e^20 + 4*(x^7 + 8*x^6 + 24*x^5 + 32*x^4 + 16*x^3)*e^15 + 6*(x^8 + 8*x^7 + 22*x^6 + 16*x
^5 - 32*x^4 - 64*x^3 - 32*x^2)*e^10 + 4*(x^9 + 8*x^8 + 18*x^7 - 16*x^6 - 128*x^5 - 192*x^4 - 96*x^3)*e^5)*e^50
- 6*(x^6 + 4*x^5 - 2*x^4 - 24*x^3 - 24*x^2 + (x^4 + 4*x^3 + 4*x^2)*e^10 + 2*(x^5 + 4*x^4 + 4*x^3)*e^5)*e^25

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maple [B]  time = 0.07, size = 90, normalized size = 3.21

method	result	size
gosper	\(x^{2} \left ({\mathrm e}^{25} x^{2} {\mathrm e}^{10}+2 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{3}+x^{4} {\mathrm e}^{25}+4 \,{\mathrm e}^{10} {\mathrm e}^{25} x +8 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{2}+4 x^{3} {\mathrm e}^{25}+4 \,{\mathrm e}^{10} {\mathrm e}^{25}+8 \,{\mathrm e}^{5} {\mathrm e}^{25} x -2 x^{2} {\mathrm e}^{25}-24 x \,{\mathrm e}^{25}-24 \,{\mathrm e}^{25}-3\right )^{2}\)	\(90\)
default	\({\mathrm e}^{50} \left ({\mathrm e}^{20} \left (x^{6}+8 x^{5}+24 x^{4}+32 x^{3}+16 x^{2}\right )+{\mathrm e}^{15} \left (4 x^{7}+32 x^{6}+96 x^{5}+128 x^{4}+64 x^{3}\right )+{\mathrm e}^{10} \left (6 x^{8}+48 x^{7}+132 x^{6}+96 x^{5}-192 x^{4}-384 x^{3}-192 x^{2}\right )+{\mathrm e}^{5} \left (4 x^{9}+32 x^{8}+72 x^{7}-64 x^{6}-512 x^{5}-768 x^{4}-384 x^{3}\right )+x^{10}+8 x^{9}+12 x^{8}-64 x^{7}-236 x^{6}-96 x^{5}+672 x^{4}+1152 x^{3}+576 x^{2}\right )+{\mathrm e}^{25} \left ({\mathrm e}^{10} \left (-6 x^{4}-24 x^{3}-24 x^{2}\right )+{\mathrm e}^{5} \left (-12 x^{5}-48 x^{4}-48 x^{3}\right )-6 x^{6}-24 x^{5}+12 x^{4}+144 x^{3}+144 x^{2}\right )+9 x^{2}\)	\(265\)
risch	\(9 x^{2}+144 x^{2} {\mathrm e}^{25}+144 x^{3} {\mathrm e}^{25}+12 x^{4} {\mathrm e}^{25}-12 \,{\mathrm e}^{25} x^{5} {\mathrm e}^{5}-48 \,{\mathrm e}^{25} x^{4} {\mathrm e}^{5}-6 \,{\mathrm e}^{25} x^{4} {\mathrm e}^{10}-24 \,{\mathrm e}^{25} x^{3} {\mathrm e}^{10}-24 \,{\mathrm e}^{25} x^{2} {\mathrm e}^{10}-6 \,{\mathrm e}^{25} x^{6}+{\mathrm e}^{50} x^{10}+4 \,{\mathrm e}^{50} x^{9} {\mathrm e}^{5}+32 \,{\mathrm e}^{50} x^{8} {\mathrm e}^{5}+6 \,{\mathrm e}^{50} x^{8} {\mathrm e}^{10}+72 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{5}+48 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{10}+4 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{15}+672 \,{\mathrm e}^{50} x^{4}+1152 \,{\mathrm e}^{50} x^{3}+576 \,{\mathrm e}^{50} x^{2}-24 \,{\mathrm e}^{25} x^{5}+8 \,{\mathrm e}^{50} x^{9}+12 \,{\mathrm e}^{50} x^{8}-64 \,{\mathrm e}^{50} x^{7}-236 \,{\mathrm e}^{50} x^{6}-96 \,{\mathrm e}^{50} x^{5}-64 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{5}+132 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{15}+{\mathrm e}^{50} x^{6} {\mathrm e}^{20}-512 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{5}+96 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{10}+96 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{15}+8 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{20}-768 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{5}-192 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{10}+128 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{15}+24 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{20}-384 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{5}-384 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{10}+64 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{15}+32 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{10}+16 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{20}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{3}\)	\(373\)
norman	\(\left (4 \,{\mathrm e}^{5} {\mathrm e}^{50}+8 \,{\mathrm e}^{50}\right ) x^{9}+\left (6 \,{\mathrm e}^{10} {\mathrm e}^{50}+32 \,{\mathrm e}^{5} {\mathrm e}^{50}+12 \,{\mathrm e}^{50}\right ) x^{8}+\left (4 \,{\mathrm e}^{15} {\mathrm e}^{50}+48 \,{\mathrm e}^{10} {\mathrm e}^{50}+72 \,{\mathrm e}^{5} {\mathrm e}^{50}-64 \,{\mathrm e}^{50}\right ) x^{7}+\left ({\mathrm e}^{20} {\mathrm e}^{50}+32 \,{\mathrm e}^{15} {\mathrm e}^{50}+132 \,{\mathrm e}^{10} {\mathrm e}^{50}-64 \,{\mathrm e}^{5} {\mathrm e}^{50}-236 \,{\mathrm e}^{50}-6 \,{\mathrm e}^{25}\right ) x^{6}+\left (16 \,{\mathrm e}^{20} {\mathrm e}^{50}-192 \,{\mathrm e}^{10} {\mathrm e}^{50}-24 \,{\mathrm e}^{10} {\mathrm e}^{25}+576 \,{\mathrm e}^{50}+144 \,{\mathrm e}^{25}+9\right ) x^{2}+\left (8 \,{\mathrm e}^{20} {\mathrm e}^{50}+96 \,{\mathrm e}^{15} {\mathrm e}^{50}+96 \,{\mathrm e}^{10} {\mathrm e}^{50}-512 \,{\mathrm e}^{5} {\mathrm e}^{50}-12 \,{\mathrm e}^{5} {\mathrm e}^{25}-96 \,{\mathrm e}^{50}-24 \,{\mathrm e}^{25}\right ) x^{5}+\left (24 \,{\mathrm e}^{20} {\mathrm e}^{50}+128 \,{\mathrm e}^{15} {\mathrm e}^{50}-192 \,{\mathrm e}^{10} {\mathrm e}^{50}-6 \,{\mathrm e}^{10} {\mathrm e}^{25}-768 \,{\mathrm e}^{5} {\mathrm e}^{50}-48 \,{\mathrm e}^{5} {\mathrm e}^{25}+672 \,{\mathrm e}^{50}+12 \,{\mathrm e}^{25}\right ) x^{4}+\left (32 \,{\mathrm e}^{20} {\mathrm e}^{50}+64 \,{\mathrm e}^{15} {\mathrm e}^{50}-384 \,{\mathrm e}^{10} {\mathrm e}^{50}-24 \,{\mathrm e}^{10} {\mathrm e}^{25}-384 \,{\mathrm e}^{5} {\mathrm e}^{50}-48 \,{\mathrm e}^{5} {\mathrm e}^{25}+1152 \,{\mathrm e}^{50}+144 \,{\mathrm e}^{25}\right ) x^{3}+{\mathrm e}^{50} x^{10}\)	\(386\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480*x^4+512*x^3+192*x^2)*exp(5)^3+(48*x^7+336*
x^6+792*x^5+480*x^4-768*x^3-1152*x^2-384*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-1152*x^
2)*exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456*x^2+1152*x)*exp(25)^2+((-24*x^3-72*x^2-4
8*x)*exp(5)^2+(-60*x^4-192*x^3-144*x^2)*exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x,method=_RET
URNVERBOSE)

[Out]

x^2*(exp(5)^2*exp(25)*x^2+2*exp(5)*exp(25)*x^3+x^4*exp(25)+4*exp(5)^2*exp(25)*x+8*exp(5)*exp(25)*x^2+4*x^3*exp
(25)+4*exp(5)^2*exp(25)+8*exp(5)*exp(25)*x-2*x^2*exp(25)-24*x*exp(25)-24*exp(25)-3)^2

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maxima [B]  time = 0.40, size = 247, normalized size = 8.82 \begin {gather*} 9 \, x^{2} + {\left (x^{10} + 8 \, x^{9} + 12 \, x^{8} - 64 \, x^{7} - 236 \, x^{6} - 96 \, x^{5} + 672 \, x^{4} + 1152 \, x^{3} + 576 \, x^{2} + {\left (x^{6} + 8 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 16 \, x^{2}\right )} e^{20} + 4 \, {\left (x^{7} + 8 \, x^{6} + 24 \, x^{5} + 32 \, x^{4} + 16 \, x^{3}\right )} e^{15} + 6 \, {\left (x^{8} + 8 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 32 \, x^{4} - 64 \, x^{3} - 32 \, x^{2}\right )} e^{10} + 4 \, {\left (x^{9} + 8 \, x^{8} + 18 \, x^{7} - 16 \, x^{6} - 128 \, x^{5} - 192 \, x^{4} - 96 \, x^{3}\right )} e^{5}\right )} e^{50} - 6 \, {\left (x^{6} + 4 \, x^{5} - 2 \, x^{4} - 24 \, x^{3} - 24 \, x^{2} + {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{10} + 2 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} e^{5}\right )} e^{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480*x^4+512*x^3+192*x^2)*exp(5)^3+(48*x^
7+336*x^6+792*x^5+480*x^4-768*x^3-1152*x^2-384*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-1
152*x^2)*exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456*x^2+1152*x)*exp(25)^2+((-24*x^3-72
*x^2-48*x)*exp(5)^2+(-60*x^4-192*x^3-144*x^2)*exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x, algo
rithm="maxima")

[Out]

9*x^2 + (x^10 + 8*x^9 + 12*x^8 - 64*x^7 - 236*x^6 - 96*x^5 + 672*x^4 + 1152*x^3 + 576*x^2 + (x^6 + 8*x^5 + 24*
x^4 + 32*x^3 + 16*x^2)*e^20 + 4*(x^7 + 8*x^6 + 24*x^5 + 32*x^4 + 16*x^3)*e^15 + 6*(x^8 + 8*x^7 + 22*x^6 + 16*x
^5 - 32*x^4 - 64*x^3 - 32*x^2)*e^10 + 4*(x^9 + 8*x^8 + 18*x^7 - 16*x^6 - 128*x^5 - 192*x^4 - 96*x^3)*e^5)*e^50
- 6*(x^6 + 4*x^5 - 2*x^4 - 24*x^3 - 24*x^2 + (x^4 + 4*x^3 + 4*x^2)*e^10 + 2*(x^5 + 4*x^4 + 4*x^3)*e^5)*e^25

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mupad [B]  time = 4.25, size = 239, normalized size = 8.54 \begin {gather*} {\mathrm {e}}^{50}\,x^{10}+\frac {{\mathrm {e}}^{50}\,\left (36\,{\mathrm {e}}^5+72\right )\,x^9}{9}+\frac {{\mathrm {e}}^{50}\,\left (256\,{\mathrm {e}}^5+48\,{\mathrm {e}}^{10}+96\right )\,x^8}{8}+\frac {{\mathrm {e}}^{50}\,\left (504\,{\mathrm {e}}^5+336\,{\mathrm {e}}^{10}+28\,{\mathrm {e}}^{15}-448\right )\,x^7}{7}+\left (\frac {{\mathrm {e}}^{50}\,\left (792\,{\mathrm {e}}^{10}-384\,{\mathrm {e}}^5+192\,{\mathrm {e}}^{15}+6\,{\mathrm {e}}^{20}-1416\right )}{6}-6\,{\mathrm {e}}^{25}\right )\,x^6+\left (\frac {{\mathrm {e}}^{50}\,\left (480\,{\mathrm {e}}^{10}-2560\,{\mathrm {e}}^5+480\,{\mathrm {e}}^{15}+40\,{\mathrm {e}}^{20}-480\right )}{5}-\frac {{\mathrm {e}}^{25}\,\left (60\,{\mathrm {e}}^5+120\right )}{5}\right )\,x^5+\left (\frac {{\mathrm {e}}^{50}\,\left (512\,{\mathrm {e}}^{15}-768\,{\mathrm {e}}^{10}-3072\,{\mathrm {e}}^5+96\,{\mathrm {e}}^{20}+2688\right )}{4}-\frac {{\mathrm {e}}^{25}\,\left (192\,{\mathrm {e}}^5+24\,{\mathrm {e}}^{10}-48\right )}{4}\right )\,x^4+\left (\frac {{\mathrm {e}}^{50}\,\left (192\,{\mathrm {e}}^{15}-1152\,{\mathrm {e}}^{10}-1152\,{\mathrm {e}}^5+96\,{\mathrm {e}}^{20}+3456\right )}{3}-\frac {{\mathrm {e}}^{25}\,\left (144\,{\mathrm {e}}^5+72\,{\mathrm {e}}^{10}-432\right )}{3}\right )\,x^3+\left (\frac {{\mathrm {e}}^{50}\,\left (32\,{\mathrm {e}}^{20}-384\,{\mathrm {e}}^{10}+1152\right )}{2}-\frac {{\mathrm {e}}^{25}\,\left (48\,{\mathrm {e}}^{10}-288\right )}{2}+9\right )\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(18*x - exp(25)*(exp(10)*(48*x + 72*x^2 + 24*x^3) - 288*x + exp(5)*(144*x^2 + 192*x^3 + 60*x^4) - 432*x^2 -
48*x^3 + 120*x^4 + 36*x^5) + exp(50)*(1152*x + exp(15)*(192*x^2 + 512*x^3 + 480*x^4 + 192*x^5 + 28*x^6) + exp
(10)*(480*x^4 - 1152*x^2 - 768*x^3 - 384*x + 792*x^5 + 336*x^6 + 48*x^7) - exp(5)*(1152*x^2 + 3072*x^3 + 2560*
x^4 + 384*x^5 - 504*x^6 - 256*x^7 - 36*x^8) + exp(20)*(32*x + 96*x^2 + 96*x^3 + 40*x^4 + 6*x^5) + 3456*x^2 + 2
688*x^3 - 480*x^4 - 1416*x^5 - 448*x^6 + 96*x^7 + 72*x^8 + 10*x^9),x)

[Out]

x^2*((exp(50)*(32*exp(20) - 384*exp(10) + 1152))/2 - (exp(25)*(48*exp(10) - 288))/2 + 9) + x^3*((exp(50)*(192*
exp(15) - 1152*exp(10) - 1152*exp(5) + 96*exp(20) + 3456))/3 - (exp(25)*(144*exp(5) + 72*exp(10) - 432))/3) +
x^4*((exp(50)*(512*exp(15) - 768*exp(10) - 3072*exp(5) + 96*exp(20) + 2688))/4 - (exp(25)*(192*exp(5) + 24*exp
(10) - 48))/4) - x^6*(6*exp(25) - (exp(50)*(792*exp(10) - 384*exp(5) + 192*exp(15) + 6*exp(20) - 1416))/6) + x
^10*exp(50) + x^5*((exp(50)*(480*exp(10) - 2560*exp(5) + 480*exp(15) + 40*exp(20) - 480))/5 - (exp(25)*(60*exp
(5) + 120))/5) + (x^7*exp(50)*(504*exp(5) + 336*exp(10) + 28*exp(15) - 448))/7 + (x^8*exp(50)*(256*exp(5) + 48
*exp(10) + 96))/8 + (x^9*exp(50)*(36*exp(5) + 72))/9

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sympy [B]  time = 0.17, size = 252, normalized size = 9.00 \begin {gather*} x^{10} e^{50} + x^{9} \left (8 e^{50} + 4 e^{55}\right ) + x^{8} \left (12 e^{50} + 32 e^{55} + 6 e^{60}\right ) + x^{7} \left (- 64 e^{50} + 72 e^{55} + 48 e^{60} + 4 e^{65}\right ) + x^{6} \left (- 64 e^{55} - 236 e^{50} - 6 e^{25} + 132 e^{60} + 32 e^{65} + e^{70}\right ) + x^{5} \left (- 512 e^{55} - 96 e^{50} - 12 e^{30} - 24 e^{25} + 96 e^{60} + 96 e^{65} + 8 e^{70}\right ) + x^{4} \left (- 192 e^{60} - 768 e^{55} - 6 e^{35} - 48 e^{30} + 12 e^{25} + 672 e^{50} + 128 e^{65} + 24 e^{70}\right ) + x^{3} \left (- 384 e^{60} - 384 e^{55} - 24 e^{35} - 48 e^{30} + 144 e^{25} + 1152 e^{50} + 64 e^{65} + 32 e^{70}\right ) + x^{2} \left (- 192 e^{60} - 24 e^{35} + 9 + 144 e^{25} + 576 e^{50} + 16 e^{70}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x**5+40*x**4+96*x**3+96*x**2+32*x)*exp(5)**4+(28*x**6+192*x**5+480*x**4+512*x**3+192*x**2)*exp(5
)**3+(48*x**7+336*x**6+792*x**5+480*x**4-768*x**3-1152*x**2-384*x)*exp(5)**2+(36*x**8+256*x**7+504*x**6-384*x*
*5-2560*x**4-3072*x**3-1152*x**2)*exp(5)+10*x**9+72*x**8+96*x**7-448*x**6-1416*x**5-480*x**4+2688*x**3+3456*x*
*2+1152*x)*exp(25)**2+((-24*x**3-72*x**2-48*x)*exp(5)**2+(-60*x**4-192*x**3-144*x**2)*exp(5)-36*x**5-120*x**4+
48*x**3+432*x**2+288*x)*exp(25)+18*x,x)

[Out]

x**10*exp(50) + x**9*(8*exp(50) + 4*exp(55)) + x**8*(12*exp(50) + 32*exp(55) + 6*exp(60)) + x**7*(-64*exp(50)
+ 72*exp(55) + 48*exp(60) + 4*exp(65)) + x**6*(-64*exp(55) - 236*exp(50) - 6*exp(25) + 132*exp(60) + 32*exp(65
) + exp(70)) + x**5*(-512*exp(55) - 96*exp(50) - 12*exp(30) - 24*exp(25) + 96*exp(60) + 96*exp(65) + 8*exp(70)
) + x**4*(-192*exp(60) - 768*exp(55) - 6*exp(35) - 48*exp(30) + 12*exp(25) + 672*exp(50) + 128*exp(65) + 24*ex
p(70)) + x**3*(-384*exp(60) - 384*exp(55) - 24*exp(35) - 48*exp(30) + 144*exp(25) + 1152*exp(50) + 64*exp(65)
+ 32*exp(70)) + x**2*(-192*exp(60) - 24*exp(35) + 9 + 144*exp(25) + 576*exp(50) + 16*exp(70))

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