3.98.71 \(\int \frac {-2560000 x^2-96000 x^3-20100 x^4-360 x^5-36 x^6+e^x (-240000+231000 x+1800 x^2+900 x^3)}{640000 x^2+24000 x^3+5025 x^4+90 x^5+9 x^6} \, dx\)

Optimal. Leaf size=25 \[ -4 x+\frac {e^x}{x \left (\frac {8}{3}+\frac {1}{100} x (5+x)\right )} \]

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Rubi [C]  time = 1.79, antiderivative size = 554, normalized size of antiderivative = 22.16, number of steps used = 29, number of rules used = 5, integrand size = 74, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.068, Rules used = {6688, 6742, 2177, 2178, 2270} \begin {gather*} \frac {3 \left (3-5 i \sqrt {15}\right ) e^{\frac {5}{6} i \left (5 \sqrt {15}+3 i\right )} \text {Ei}\left (\frac {1}{6} \left (6 x+5 \left (3-5 i \sqrt {15}\right )\right )\right )}{2000}-\frac {3 \left (125-3 i \sqrt {15}\right ) e^{\frac {5}{6} i \left (5 \sqrt {15}+3 i\right )} \text {Ei}\left (\frac {1}{6} \left (6 x+5 \left (3-5 i \sqrt {15}\right )\right )\right )}{2000}+\frac {3}{200} i \sqrt {\frac {3}{5}} e^{\frac {5}{6} i \left (5 \sqrt {15}+3 i\right )} \text {Ei}\left (\frac {1}{6} \left (6 x+5 \left (3-5 i \sqrt {15}\right )\right )\right )+\frac {183 e^{\frac {5}{6} i \left (5 \sqrt {15}+3 i\right )} \text {Ei}\left (\frac {1}{6} \left (6 x+5 \left (3-5 i \sqrt {15}\right )\right )\right )}{1000}+\frac {3 \left (3+5 i \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (6 x+5 \left (3+5 i \sqrt {15}\right )\right )\right )}{2000}-\frac {3 \left (125+3 i \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (6 x+5 \left (3+5 i \sqrt {15}\right )\right )\right )}{2000}-\frac {3}{200} i \sqrt {\frac {3}{5}} e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (6 x+5 \left (3+5 i \sqrt {15}\right )\right )\right )+\frac {183 e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (6 x+5 \left (3+5 i \sqrt {15}\right )\right )\right )}{1000}-4 x-\frac {9 \left (3-5 i \sqrt {15}\right ) e^x}{1000 \left (6 x+5 \left (3-5 i \sqrt {15}\right )\right )}-\frac {549 e^x}{500 \left (6 x+5 \left (3-5 i \sqrt {15}\right )\right )}-\frac {9 \left (3+5 i \sqrt {15}\right ) e^x}{1000 \left (6 x+5 \left (3+5 i \sqrt {15}\right )\right )}-\frac {549 e^x}{500 \left (6 x+5 \left (3+5 i \sqrt {15}\right )\right )}+\frac {3 e^x}{8 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2560000*x^2 - 96000*x^3 - 20100*x^4 - 360*x^5 - 36*x^6 + E^x*(-240000 + 231000*x + 1800*x^2 + 900*x^3))/
(640000*x^2 + 24000*x^3 + 5025*x^4 + 90*x^5 + 9*x^6),x]

[Out]

(3*E^x)/(8*x) - 4*x - (549*E^x)/(500*(5*(3 - (5*I)*Sqrt[15]) + 6*x)) - (9*(3 - (5*I)*Sqrt[15])*E^x)/(1000*(5*(
3 - (5*I)*Sqrt[15]) + 6*x)) - (549*E^x)/(500*(5*(3 + (5*I)*Sqrt[15]) + 6*x)) - (9*(3 + (5*I)*Sqrt[15])*E^x)/(1
000*(5*(3 + (5*I)*Sqrt[15]) + 6*x)) + (183*E^(((5*I)/6)*(3*I + 5*Sqrt[15]))*ExpIntegralEi[(5*(3 - (5*I)*Sqrt[1
5]) + 6*x)/6])/1000 + ((3*I)/200)*Sqrt[3/5]*E^(((5*I)/6)*(3*I + 5*Sqrt[15]))*ExpIntegralEi[(5*(3 - (5*I)*Sqrt[
15]) + 6*x)/6] - (3*(125 - (3*I)*Sqrt[15])*E^(((5*I)/6)*(3*I + 5*Sqrt[15]))*ExpIntegralEi[(5*(3 - (5*I)*Sqrt[1
5]) + 6*x)/6])/2000 + (3*(3 - (5*I)*Sqrt[15])*E^(((5*I)/6)*(3*I + 5*Sqrt[15]))*ExpIntegralEi[(5*(3 - (5*I)*Sqr
t[15]) + 6*x)/6])/2000 + (183*ExpIntegralEi[(5*(3 + (5*I)*Sqrt[15]) + 6*x)/6])/(1000*E^((5*(3 + (5*I)*Sqrt[15]
))/6)) - (((3*I)/200)*Sqrt[3/5]*ExpIntegralEi[(5*(3 + (5*I)*Sqrt[15]) + 6*x)/6])/E^((5*(3 + (5*I)*Sqrt[15]))/6
) - (3*(125 + (3*I)*Sqrt[15])*ExpIntegralEi[(5*(3 + (5*I)*Sqrt[15]) + 6*x)/6])/(2000*E^((5*(3 + (5*I)*Sqrt[15]
))/6)) + (3*(3 + (5*I)*Sqrt[15])*ExpIntegralEi[(5*(3 + (5*I)*Sqrt[15]) + 6*x)/6])/(2000*E^((5*(3 + (5*I)*Sqrt[
15]))/6))

Rule 2177

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_), x_Symbol] :> Simp[((c + d*x)^(m
+ 1)*(b*F^(g*(e + f*x)))^n)/(d*(m + 1)), x] - Dist[(f*g*n*Log[F])/(d*(m + 1)), Int[(c + d*x)^(m + 1)*(b*F^(g*
(e + f*x)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && LtQ[m, -1] && IntegerQ[2*m] &&  !$UseGamma ===
True

Rule 2178

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[(F^(g*(e - (c*f)/d))*ExpIntegral
Ei[(f*g*(c + d*x)*Log[F])/d])/d, x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !$UseGamma === True

Rule 2270

Int[((F_)^((g_.)*((d_.) + (e_.)*(x_))^(n_.))*(u_)^(m_.))/((a_.) + (b_.)*(x_) + (c_)*(x_)^2), x_Symbol] :> Int[
ExpandIntegrand[F^(g*(d + e*x)^n), u^m/(a + b*x + c*x^2), x], x] /; FreeQ[{F, a, b, c, d, e, g, n}, x] && Poly
nomialQ[u, x] && IntegerQ[m]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-4+\frac {300 e^x \left (-800+770 x+6 x^2+3 x^3\right )}{x^2 \left (800+15 x+3 x^2\right )^2}\right ) \, dx\\ &=-4 x+300 \int \frac {e^x \left (-800+770 x+6 x^2+3 x^3\right )}{x^2 \left (800+15 x+3 x^2\right )^2} \, dx\\ &=-4 x+300 \int \left (-\frac {e^x}{800 x^2}+\frac {e^x}{800 x}+\frac {3 e^x (-305+3 x)}{160 \left (800+15 x+3 x^2\right )^2}-\frac {3 e^x (4+x)}{800 \left (800+15 x+3 x^2\right )}\right ) \, dx\\ &=-4 x-\frac {3}{8} \int \frac {e^x}{x^2} \, dx+\frac {3}{8} \int \frac {e^x}{x} \, dx-\frac {9}{8} \int \frac {e^x (4+x)}{800+15 x+3 x^2} \, dx+\frac {45}{8} \int \frac {e^x (-305+3 x)}{\left (800+15 x+3 x^2\right )^2} \, dx\\ &=\frac {3 e^x}{8 x}-4 x+\frac {3 \text {Ei}(x)}{8}-\frac {3}{8} \int \frac {e^x}{x} \, dx-\frac {9}{8} \int \left (\frac {\left (1-\frac {3}{25} i \sqrt {\frac {3}{5}}\right ) e^x}{15-25 i \sqrt {15}+6 x}+\frac {\left (1+\frac {3}{25} i \sqrt {\frac {3}{5}}\right ) e^x}{15+25 i \sqrt {15}+6 x}\right ) \, dx+\frac {45}{8} \int \left (-\frac {305 e^x}{\left (800+15 x+3 x^2\right )^2}+\frac {3 e^x x}{\left (800+15 x+3 x^2\right )^2}\right ) \, dx\\ &=\frac {3 e^x}{8 x}-4 x+\frac {135}{8} \int \frac {e^x x}{\left (800+15 x+3 x^2\right )^2} \, dx-\frac {13725}{8} \int \frac {e^x}{\left (800+15 x+3 x^2\right )^2} \, dx-\frac {\left (9 \left (125-3 i \sqrt {15}\right )\right ) \int \frac {e^x}{15-25 i \sqrt {15}+6 x} \, dx}{1000}-\frac {\left (9 \left (125+3 i \sqrt {15}\right )\right ) \int \frac {e^x}{15+25 i \sqrt {15}+6 x} \, dx}{1000}\\ &=\frac {3 e^x}{8 x}-4 x-\frac {3 \left (125-3 i \sqrt {15}\right ) e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )\right )}{2000}-\frac {3 \left (125+3 i \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )\right )}{2000}+\frac {135}{8} \int \left (-\frac {2 \left (-15+25 i \sqrt {15}\right ) e^x}{3125 \left (-15+25 i \sqrt {15}-6 x\right )^2}-\frac {2 i \sqrt {\frac {3}{5}} e^x}{15625 \left (-15+25 i \sqrt {15}-6 x\right )}-\frac {2 \left (-15-25 i \sqrt {15}\right ) e^x}{3125 \left (15+25 i \sqrt {15}+6 x\right )^2}-\frac {2 i \sqrt {\frac {3}{5}} e^x}{15625 \left (15+25 i \sqrt {15}+6 x\right )}\right ) \, dx-\frac {13725}{8} \int \left (-\frac {12 e^x}{3125 \left (-15+25 i \sqrt {15}-6 x\right )^2}+\frac {4 i \sqrt {\frac {3}{5}} e^x}{78125 \left (-15+25 i \sqrt {15}-6 x\right )}-\frac {12 e^x}{3125 \left (15+25 i \sqrt {15}+6 x\right )^2}+\frac {4 i \sqrt {\frac {3}{5}} e^x}{78125 \left (15+25 i \sqrt {15}+6 x\right )}\right ) \, dx\\ &=\frac {3 e^x}{8 x}-4 x-\frac {3 \left (125-3 i \sqrt {15}\right ) e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )\right )}{2000}-\frac {3 \left (125+3 i \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )\right )}{2000}+\frac {1647}{250} \int \frac {e^x}{\left (-15+25 i \sqrt {15}-6 x\right )^2} \, dx+\frac {1647}{250} \int \frac {e^x}{\left (15+25 i \sqrt {15}+6 x\right )^2} \, dx-\frac {\left (27 i \sqrt {\frac {3}{5}}\right ) \int \frac {e^x}{-15+25 i \sqrt {15}-6 x} \, dx}{12500}-\frac {\left (27 i \sqrt {\frac {3}{5}}\right ) \int \frac {e^x}{15+25 i \sqrt {15}+6 x} \, dx}{12500}-\frac {\left (549 i \sqrt {\frac {3}{5}}\right ) \int \frac {e^x}{-15+25 i \sqrt {15}-6 x} \, dx}{6250}-\frac {\left (549 i \sqrt {\frac {3}{5}}\right ) \int \frac {e^x}{15+25 i \sqrt {15}+6 x} \, dx}{6250}+\frac {1}{500} \left (27 \left (3-5 i \sqrt {15}\right )\right ) \int \frac {e^x}{\left (-15+25 i \sqrt {15}-6 x\right )^2} \, dx+\frac {1}{500} \left (27 \left (3+5 i \sqrt {15}\right )\right ) \int \frac {e^x}{\left (15+25 i \sqrt {15}+6 x\right )^2} \, dx\\ &=\frac {3 e^x}{8 x}-4 x-\frac {549 e^x}{500 \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )}-\frac {9 \left (3-5 i \sqrt {15}\right ) e^x}{1000 \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )}-\frac {549 e^x}{500 \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )}-\frac {9 \left (3+5 i \sqrt {15}\right ) e^x}{1000 \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )}+\frac {3}{200} i \sqrt {\frac {3}{5}} e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )\right )-\frac {3 \left (125-3 i \sqrt {15}\right ) e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )\right )}{2000}-\frac {3}{200} i \sqrt {\frac {3}{5}} e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )\right )-\frac {3 \left (125+3 i \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )\right )}{2000}-\frac {549}{500} \int \frac {e^x}{-15+25 i \sqrt {15}-6 x} \, dx+\frac {549}{500} \int \frac {e^x}{15+25 i \sqrt {15}+6 x} \, dx-\frac {\left (9 \left (3-5 i \sqrt {15}\right )\right ) \int \frac {e^x}{-15+25 i \sqrt {15}-6 x} \, dx}{1000}+\frac {\left (9 \left (3+5 i \sqrt {15}\right )\right ) \int \frac {e^x}{15+25 i \sqrt {15}+6 x} \, dx}{1000}\\ &=\frac {3 e^x}{8 x}-4 x-\frac {549 e^x}{500 \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )}-\frac {9 \left (3-5 i \sqrt {15}\right ) e^x}{1000 \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )}-\frac {549 e^x}{500 \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )}-\frac {9 \left (3+5 i \sqrt {15}\right ) e^x}{1000 \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )}+\frac {183 e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )\right )}{1000}+\frac {3}{200} i \sqrt {\frac {3}{5}} e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )\right )-\frac {3 \left (125-3 i \sqrt {15}\right ) e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )\right )}{2000}+\frac {3 \left (3-5 i \sqrt {15}\right ) e^{\frac {5}{6} i \left (3 i+5 \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3-5 i \sqrt {15}\right )+6 x\right )\right )}{2000}+\frac {183 e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )\right )}{1000}-\frac {3}{200} i \sqrt {\frac {3}{5}} e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )\right )-\frac {3 \left (125+3 i \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )\right )}{2000}+\frac {3 \left (3+5 i \sqrt {15}\right ) e^{-\frac {5}{6} \left (3+5 i \sqrt {15}\right )} \text {Ei}\left (\frac {1}{6} \left (5 \left (3+5 i \sqrt {15}\right )+6 x\right )\right )}{2000}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.35, size = 36, normalized size = 1.44 \begin {gather*} -4 x+300 e^x \left (\frac {1}{800 x}-\frac {3 (5+x)}{800 \left (800+15 x+3 x^2\right )}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2560000*x^2 - 96000*x^3 - 20100*x^4 - 360*x^5 - 36*x^6 + E^x*(-240000 + 231000*x + 1800*x^2 + 900*
x^3))/(640000*x^2 + 24000*x^3 + 5025*x^4 + 90*x^5 + 9*x^6),x]

[Out]

-4*x + 300*E^x*(1/(800*x) - (3*(5 + x))/(800*(800 + 15*x + 3*x^2)))

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fricas [A]  time = 0.76, size = 38, normalized size = 1.52 \begin {gather*} -\frac {4 \, {\left (3 \, x^{4} + 15 \, x^{3} + 800 \, x^{2} - 75 \, e^{x}\right )}}{3 \, x^{3} + 15 \, x^{2} + 800 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100*x^4-96000*x^3-2560000*x^2)/(9*x^6+90
*x^5+5025*x^4+24000*x^3+640000*x^2),x, algorithm="fricas")

[Out]

-4*(3*x^4 + 15*x^3 + 800*x^2 - 75*e^x)/(3*x^3 + 15*x^2 + 800*x)

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giac [A]  time = 0.13, size = 38, normalized size = 1.52 \begin {gather*} -\frac {4 \, {\left (3 \, x^{4} + 15 \, x^{3} + 800 \, x^{2} - 75 \, e^{x}\right )}}{3 \, x^{3} + 15 \, x^{2} + 800 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100*x^4-96000*x^3-2560000*x^2)/(9*x^6+90
*x^5+5025*x^4+24000*x^3+640000*x^2),x, algorithm="giac")

[Out]

-4*(3*x^4 + 15*x^3 + 800*x^2 - 75*e^x)/(3*x^3 + 15*x^2 + 800*x)

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maple [A]  time = 0.10, size = 24, normalized size = 0.96

method	result	size
risch	\(-4 x +\frac {300 \,{\mathrm e}^{x}}{x \left (3 x^{2}+15 x +800\right )}\)	\(24\)
norman	\(\frac {-2900 x^{2}+16000 x -12 x^{4}+300 \,{\mathrm e}^{x}}{x \left (3 x^{2}+15 x +800\right )}\)	\(35\)
default	\(-\frac {4096 \left (6 x +15\right )}{15 \left (3 x^{2}+15 x +800\right )}-\frac {256 \left (-15 x -1600\right )}{25 \left (3 x^{2}+15 x +800\right )}-\frac {20100 \left (-\frac {61 x}{1125}+\frac {32}{225}\right )}{x^{2}+5 x +\frac {800}{3}}-\frac {360 \left (\frac {31 x}{75}+\frac {1952}{135}\right )}{x^{2}+5 x +\frac {800}{3}}-4 x +\frac {-\frac {6692 x}{15}+3968}{x^{2}+5 x +\frac {800}{3}}+\frac {3 \,{\mathrm e}^{x} \left (279 x^{2}+1635 x +50000\right )}{500 \left (3 x^{2}+15 x +800\right ) x}-\frac {231 \,{\mathrm e}^{x} \left (3 x -305\right )}{500 \left (3 x^{2}+15 x +800\right )}+\frac {72 \,{\mathrm e}^{x} \left (5+2 x \right )}{125 \left (3 x^{2}+15 x +800\right )}-\frac {12 \,{\mathrm e}^{x} \left (3 x +320\right )}{25 \left (3 x^{2}+15 x +800\right )}\)	\(186\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100*x^4-96000*x^3-2560000*x^2)/(9*x^6+90*x^5+5
025*x^4+24000*x^3+640000*x^2),x,method=_RETURNVERBOSE)

[Out]

-4*x+300/x/(3*x^2+15*x+800)*exp(x)

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maxima [B]  time = 0.48, size = 119, normalized size = 4.76 \begin {gather*} -4 \, x - \frac {4 \, {\left (1673 \, x - 14880\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} - \frac {8 \, {\left (279 \, x + 9760\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} + \frac {268 \, {\left (61 \, x - 160\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} + \frac {256 \, {\left (3 \, x + 320\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} - \frac {4096 \, {\left (2 \, x + 5\right )}}{5 \, {\left (3 \, x^{2} + 15 \, x + 800\right )}} + \frac {300 \, e^{x}}{3 \, x^{3} + 15 \, x^{2} + 800 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((900*x^3+1800*x^2+231000*x-240000)*exp(x)-36*x^6-360*x^5-20100*x^4-96000*x^3-2560000*x^2)/(9*x^6+90
*x^5+5025*x^4+24000*x^3+640000*x^2),x, algorithm="maxima")

[Out]

-4*x - 4/5*(1673*x - 14880)/(3*x^2 + 15*x + 800) - 8/5*(279*x + 9760)/(3*x^2 + 15*x + 800) + 268/5*(61*x - 160
)/(3*x^2 + 15*x + 800) + 256/5*(3*x + 320)/(3*x^2 + 15*x + 800) - 4096/5*(2*x + 5)/(3*x^2 + 15*x + 800) + 300*
e^x/(3*x^3 + 15*x^2 + 800*x)

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mupad [B]  time = 5.86, size = 23, normalized size = 0.92 \begin {gather*} \frac {300\,{\mathrm {e}}^x}{x\,\left (3\,x^2+15\,x+800\right )}-4\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2560000*x^2 + 96000*x^3 + 20100*x^4 + 360*x^5 + 36*x^6 - exp(x)*(231000*x + 1800*x^2 + 900*x^3 - 240000)
)/(640000*x^2 + 24000*x^3 + 5025*x^4 + 90*x^5 + 9*x^6),x)

[Out]

(300*exp(x))/(x*(15*x + 3*x^2 + 800)) - 4*x

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sympy [A]  time = 0.14, size = 20, normalized size = 0.80 \begin {gather*} - 4 x + \frac {300 e^{x}}{3 x^{3} + 15 x^{2} + 800 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((900*x**3+1800*x**2+231000*x-240000)*exp(x)-36*x**6-360*x**5-20100*x**4-96000*x**3-2560000*x**2)/(9
*x**6+90*x**5+5025*x**4+24000*x**3+640000*x**2),x)

[Out]

-4*x + 300*exp(x)/(3*x**3 + 15*x**2 + 800*x)

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