3.96.11 \(\int e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} (200 x^2+150 x^4)+e^{2 x} (-400 x^3-100 x^5)+e^x (400 x^2+200 x^4+25 x^6)} (e^{5 x} (50 x+125 x^2)+e^{4 x} (-300 x^2-400 x^3)+e^{3 x} (400 x+600 x^2+600 x^3+450 x^4)+e^{2 x} (-1200 x^2-800 x^3-500 x^4-200 x^5)+e^x (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6)) \, dx\)

Optimal. Leaf size=30 \[ e^{-3-x+x \left (1+25 e^x x \left (4+\left (-e^x+x\right )^2\right )^2\right )} \]

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Rubi [F]  time = 28.72, 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 \exp \left (-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-3 + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^
x*(400*x^2 + 200*x^4 + 25*x^6))*(E^(5*x)*(50*x + 125*x^2) + E^(4*x)*(-300*x^2 - 400*x^3) + E^(3*x)*(400*x + 60
0*x^2 + 600*x^3 + 450*x^4) + E^(2*x)*(-1200*x^2 - 800*x^3 - 500*x^4 - 200*x^5) + E^x*(800*x + 400*x^2 + 800*x^
3 + 200*x^4 + 150*x^5 + 25*x^6)),x]

[Out]

800*Defer[Int][E^(-3 + x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3
- 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x, x] + 400*Defer[Int][E^(-3 + 3*x + 25*E^(5*x)*x^2 - 100*E^(4*
x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x, x]
+ 50*Defer[Int][E^(-3 + 5*x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x
^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x, x] + 400*Defer[Int][E^(-3 + x + 25*E^(5*x)*x^2 - 100*E^(4
*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^2,
x] - 1200*Defer[Int][E^(-3 + 2*x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-
400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^2, x] + 600*Defer[Int][E^(-3 + 3*x + 25*E^(5*x)*x^2 -
100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^
6))*x^2, x] - 300*Defer[Int][E^(-3 + 4*x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^
(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^2, x] + 125*Defer[Int][E^(-3 + 5*x + 25*E^(5*
x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4
+ 25*x^6))*x^2, x] + 800*Defer[Int][E^(-3 + x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4
) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^3, x] - 800*Defer[Int][E^(-3 + 2*x + 25
*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 2
00*x^4 + 25*x^6))*x^3, x] + 600*Defer[Int][E^(-3 + 3*x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 +
150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^3, x] - 400*Defer[Int][E^(-3 +
4*x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400
*x^2 + 200*x^4 + 25*x^6))*x^3, x] + 200*Defer[Int][E^(-3 + x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200
*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^4, x] - 500*Defer[Int][E^
(-3 + 2*x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^
x*(400*x^2 + 200*x^4 + 25*x^6))*x^4, x] + 450*Defer[Int][E^(-3 + 3*x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3
*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^4, x] + 150*Defer
[Int][E^(-3 + x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5
) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^5, x] - 200*Defer[Int][E^(-3 + 2*x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3
+ E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^5, x] + 25*
Defer[Int][E^(-3 + x + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 10
0*x^5) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*x^6, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-100 \exp \left (-3+4 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x^2 (3+4 x)+25 \exp \left (-3+5 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x (2+5 x)-100 \exp \left (-3+2 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x^2 \left (12+8 x+5 x^2+2 x^3\right )+50 \exp \left (-3+3 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x \left (8+12 x+12 x^2+9 x^3\right )+25 \exp \left (-3+x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x \left (32+16 x+32 x^2+8 x^3+6 x^4+x^5\right )\right ) \, dx\\ &=25 \int \exp \left (-3+5 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x (2+5 x) \, dx+25 \int \exp \left (-3+x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x \left (32+16 x+32 x^2+8 x^3+6 x^4+x^5\right ) \, dx+50 \int \exp \left (-3+3 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x \left (8+12 x+12 x^2+9 x^3\right ) \, dx-100 \int \exp \left (-3+4 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x^2 (3+4 x) \, dx-100 \int \exp \left (-3+2 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x^2 \left (12+8 x+5 x^2+2 x^3\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.14, size = 71, normalized size = 2.37 \begin {gather*} e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3-100 e^{2 x} x^3 \left (4+x^2\right )+25 e^x x^2 \left (4+x^2\right )^2+50 e^{3 x} x^2 \left (4+3 x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-3 + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 + E^(3*x)*(200*x^2 + 150*x^4) + E^(2*x)*(-400*x^3 - 100*x^5
) + E^x*(400*x^2 + 200*x^4 + 25*x^6))*(E^(5*x)*(50*x + 125*x^2) + E^(4*x)*(-300*x^2 - 400*x^3) + E^(3*x)*(400*
x + 600*x^2 + 600*x^3 + 450*x^4) + E^(2*x)*(-1200*x^2 - 800*x^3 - 500*x^4 - 200*x^5) + E^x*(800*x + 400*x^2 +
800*x^3 + 200*x^4 + 150*x^5 + 25*x^6)),x]

[Out]

E^(-3 + 25*E^(5*x)*x^2 - 100*E^(4*x)*x^3 - 100*E^(2*x)*x^3*(4 + x^2) + 25*E^x*x^2*(4 + x^2)^2 + 50*E^(3*x)*x^2
*(4 + 3*x^2))

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fricas [B]  time = 0.51, size = 71, normalized size = 2.37 \begin {gather*} e^{\left (-100 \, x^{3} e^{\left (4 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 50 \, {\left (3 \, x^{4} + 4 \, x^{2}\right )} e^{\left (3 \, x\right )} - 100 \, {\left (x^{5} + 4 \, x^{3}\right )} e^{\left (2 \, x\right )} + 25 \, {\left (x^{6} + 8 \, x^{4} + 16 \, x^{2}\right )} e^{x} - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+600*x^3+600*x^2+400*x)*exp(x)^3+(-200*
x^5-500*x^4-800*x^3-1200*x^2)*exp(x)^2+(25*x^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x
)^5-100*x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+(25*x^6+200*x^4+400*x^2)*exp(x)-3)
,x, algorithm="fricas")

[Out]

e^(-100*x^3*e^(4*x) + 25*x^2*e^(5*x) + 50*(3*x^4 + 4*x^2)*e^(3*x) - 100*(x^5 + 4*x^3)*e^(2*x) + 25*(x^6 + 8*x^
4 + 16*x^2)*e^x - 3)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 25 \, {\left ({\left (5 \, x^{2} + 2 \, x\right )} e^{\left (5 \, x\right )} - 4 \, {\left (4 \, x^{3} + 3 \, x^{2}\right )} e^{\left (4 \, x\right )} + 2 \, {\left (9 \, x^{4} + 12 \, x^{3} + 12 \, x^{2} + 8 \, x\right )} e^{\left (3 \, x\right )} - 4 \, {\left (2 \, x^{5} + 5 \, x^{4} + 8 \, x^{3} + 12 \, x^{2}\right )} e^{\left (2 \, x\right )} + {\left (x^{6} + 6 \, x^{5} + 8 \, x^{4} + 32 \, x^{3} + 16 \, x^{2} + 32 \, x\right )} e^{x}\right )} e^{\left (-100 \, x^{3} e^{\left (4 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 50 \, {\left (3 \, x^{4} + 4 \, x^{2}\right )} e^{\left (3 \, x\right )} - 100 \, {\left (x^{5} + 4 \, x^{3}\right )} e^{\left (2 \, x\right )} + 25 \, {\left (x^{6} + 8 \, x^{4} + 16 \, x^{2}\right )} e^{x} - 3\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+600*x^3+600*x^2+400*x)*exp(x)^3+(-200*
x^5-500*x^4-800*x^3-1200*x^2)*exp(x)^2+(25*x^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x
)^5-100*x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+(25*x^6+200*x^4+400*x^2)*exp(x)-3)
,x, algorithm="giac")

[Out]

integrate(25*((5*x^2 + 2*x)*e^(5*x) - 4*(4*x^3 + 3*x^2)*e^(4*x) + 2*(9*x^4 + 12*x^3 + 12*x^2 + 8*x)*e^(3*x) -
4*(2*x^5 + 5*x^4 + 8*x^3 + 12*x^2)*e^(2*x) + (x^6 + 6*x^5 + 8*x^4 + 32*x^3 + 16*x^2 + 32*x)*e^x)*e^(-100*x^3*e
^(4*x) + 25*x^2*e^(5*x) + 50*(3*x^4 + 4*x^2)*e^(3*x) - 100*(x^5 + 4*x^3)*e^(2*x) + 25*(x^6 + 8*x^4 + 16*x^2)*e
^x - 3), x)

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maple [B]  time = 0.14, size = 79, normalized size = 2.63

method	result	size
risch	\({\mathrm e}^{25 x^{6} {\mathrm e}^{x}-100 x^{5} {\mathrm e}^{2 x}+200 \,{\mathrm e}^{x} x^{4}+150 \,{\mathrm e}^{3 x} x^{4}-400 \,{\mathrm e}^{2 x} x^{3}-100 x^{3} {\mathrm e}^{4 x}+400 \,{\mathrm e}^{x} x^{2}+25 x^{2} {\mathrm e}^{5 x}+200 x^{2} {\mathrm e}^{3 x}-3}\)	\(79\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+600*x^3+600*x^2+400*x)*exp(x)^3+(-200*x^5-50
0*x^4-800*x^3-1200*x^2)*exp(x)^2+(25*x^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x)^5-10
0*x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+(25*x^6+200*x^4+400*x^2)*exp(x)-3),x,met
hod=_RETURNVERBOSE)

[Out]

exp(25*x^6*exp(x)-100*x^5*exp(2*x)+200*exp(x)*x^4+150*exp(3*x)*x^4-400*exp(2*x)*x^3-100*x^3*exp(4*x)+400*exp(x
)*x^2+25*x^2*exp(5*x)+200*x^2*exp(3*x)-3)

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maxima [B]  time = 0.74, size = 78, normalized size = 2.60 \begin {gather*} e^{\left (25 \, x^{6} e^{x} - 100 \, x^{5} e^{\left (2 \, x\right )} + 150 \, x^{4} e^{\left (3 \, x\right )} + 200 \, x^{4} e^{x} - 100 \, x^{3} e^{\left (4 \, x\right )} - 400 \, x^{3} e^{\left (2 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 200 \, x^{2} e^{\left (3 \, x\right )} + 400 \, x^{2} e^{x} - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((125*x^2+50*x)*exp(x)^5+(-400*x^3-300*x^2)*exp(x)^4+(450*x^4+600*x^3+600*x^2+400*x)*exp(x)^3+(-200*
x^5-500*x^4-800*x^3-1200*x^2)*exp(x)^2+(25*x^6+150*x^5+200*x^4+800*x^3+400*x^2+800*x)*exp(x))*exp(25*x^2*exp(x
)^5-100*x^3*exp(x)^4+(150*x^4+200*x^2)*exp(x)^3+(-100*x^5-400*x^3)*exp(x)^2+(25*x^6+200*x^4+400*x^2)*exp(x)-3)
,x, algorithm="maxima")

[Out]

e^(25*x^6*e^x - 100*x^5*e^(2*x) + 150*x^4*e^(3*x) + 200*x^4*e^x - 100*x^3*e^(4*x) - 400*x^3*e^(2*x) + 25*x^2*e
^(5*x) + 200*x^2*e^(3*x) + 400*x^2*e^x - 3)

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mupad [B]  time = 8.33, size = 87, normalized size = 2.90 \begin {gather*} {\mathrm {e}}^{-3}\,{\mathrm {e}}^{25\,x^6\,{\mathrm {e}}^x}\,{\mathrm {e}}^{200\,x^4\,{\mathrm {e}}^x}\,{\mathrm {e}}^{400\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{25\,x^2\,{\mathrm {e}}^{5\,x}}\,{\mathrm {e}}^{-100\,x^3\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-100\,x^5\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{150\,x^4\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{200\,x^2\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{-400\,x^3\,{\mathrm {e}}^{2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(x)*(400*x^2 + 200*x^4 + 25*x^6) + exp(3*x)*(200*x^2 + 150*x^4) - exp(2*x)*(400*x^3 + 100*x^5) + 25
*x^2*exp(5*x) - 100*x^3*exp(4*x) - 3)*(exp(5*x)*(50*x + 125*x^2) - exp(4*x)*(300*x^2 + 400*x^3) + exp(3*x)*(40
0*x + 600*x^2 + 600*x^3 + 450*x^4) + exp(x)*(800*x + 400*x^2 + 800*x^3 + 200*x^4 + 150*x^5 + 25*x^6) - exp(2*x
)*(1200*x^2 + 800*x^3 + 500*x^4 + 200*x^5)),x)

[Out]

exp(-3)*exp(25*x^6*exp(x))*exp(200*x^4*exp(x))*exp(400*x^2*exp(x))*exp(25*x^2*exp(5*x))*exp(-100*x^3*exp(4*x))
*exp(-100*x^5*exp(2*x))*exp(150*x^4*exp(3*x))*exp(200*x^2*exp(3*x))*exp(-400*x^3*exp(2*x))

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sympy [B]  time = 0.60, size = 73, normalized size = 2.43 \begin {gather*} e^{- 100 x^{3} e^{4 x} + 25 x^{2} e^{5 x} + \left (150 x^{4} + 200 x^{2}\right ) e^{3 x} + \left (- 100 x^{5} - 400 x^{3}\right ) e^{2 x} + \left (25 x^{6} + 200 x^{4} + 400 x^{2}\right ) e^{x} - 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((125*x**2+50*x)*exp(x)**5+(-400*x**3-300*x**2)*exp(x)**4+(450*x**4+600*x**3+600*x**2+400*x)*exp(x)*
*3+(-200*x**5-500*x**4-800*x**3-1200*x**2)*exp(x)**2+(25*x**6+150*x**5+200*x**4+800*x**3+400*x**2+800*x)*exp(x
))*exp(25*x**2*exp(x)**5-100*x**3*exp(x)**4+(150*x**4+200*x**2)*exp(x)**3+(-100*x**5-400*x**3)*exp(x)**2+(25*x
**6+200*x**4+400*x**2)*exp(x)-3),x)

[Out]

exp(-100*x**3*exp(4*x) + 25*x**2*exp(5*x) + (150*x**4 + 200*x**2)*exp(3*x) + (-100*x**5 - 400*x**3)*exp(2*x) +
(25*x**6 + 200*x**4 + 400*x**2)*exp(x) - 3)

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