3.11.98 \(\int \frac {e^x (-12+12 x+512 x^3-128 x^4)+e^{\frac {1}{4} (20+3 x)} (-12+9 x+512 x^3-96 x^4)}{8 e^{2 x}+8 e^{\frac {1}{2} (20+3 x)}+16 e^{x+\frac {1}{4} (20+3 x)}} \, dx\)

Optimal. Leaf size=27 \[ \frac {-\frac {3 x}{2}+16 x^4}{e^{5+\frac {3 x}{4}}+e^x} \]

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Rubi [F]  time = 2.89, 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 \frac {e^x \left (-12+12 x+512 x^3-128 x^4\right )+e^{\frac {1}{4} (20+3 x)} \left (-12+9 x+512 x^3-96 x^4\right )}{8 e^{2 x}+8 e^{\frac {1}{2} (20+3 x)}+16 e^{x+\frac {1}{4} (20+3 x)}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^x*(-12 + 12*x + 512*x^3 - 128*x^4) + E^((20 + 3*x)/4)*(-12 + 9*x + 512*x^3 - 96*x^4))/(8*E^(2*x) + 8*E^
((20 + 3*x)/2) + 16*E^(x + (20 + 3*x)/4)),x]

[Out]

-E^(10 - (3*x)/2) + (6*E^(5 - (5*x)/4))/5 + 2*E^(-5 - (3*x)/4) - 3*E^(-10 - x/2) + 6*E^(-15 - x/4) - 3/(2*E^x)
+ (3*x)/(2*E^20) - (3*E^(10 - (3*x)/2)*x)/2 + (3*E^(5 - (5*x)/4)*x)/2 - (3*x)/(2*E^x) + 16*E^(10 - (3*x)/2)*x
^4 - 16*E^(5 - (5*x)/4)*x^4 + (16*x^4)/E^x - (6*Log[E^5 + E^(x/4)])/E^20 + (3*Defer[Int][(E^(20 - (3*x)/2)*x)/
(E^5 + E^(x/4))^2, x])/8 - (21*Defer[Int][(E^(15 - (3*x)/2)*x)/(E^5 + E^(x/4)), x])/8 - 64*Defer[Int][(E^(15 -
(3*x)/2)*x^3)/(E^5 + E^(x/4)), x] - 4*Defer[Int][(E^(20 - (3*x)/2)*x^4)/(E^5 + E^(x/4))^2, x] + 28*Defer[Int]
[(E^(15 - (3*x)/2)*x^4)/(E^5 + E^(x/4)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-3 x/2} \left (e^x \left (-12+12 x+512 x^3-128 x^4\right )+e^{\frac {1}{4} (20+3 x)} \left (-12+9 x+512 x^3-96 x^4\right )\right )}{8 \left (e^5+e^{x/4}\right )^2} \, dx\\ &=\frac {1}{8} \int \frac {e^{-3 x/2} \left (e^x \left (-12+12 x+512 x^3-128 x^4\right )+e^{\frac {1}{4} (20+3 x)} \left (-12+9 x+512 x^3-96 x^4\right )\right )}{\left (e^5+e^{x/4}\right )^2} \, dx\\ &=\frac {1}{8} \int \left (-\frac {e^{20-\frac {3 x}{2}} x \left (-3+32 x^3\right )}{\left (e^5+e^{x/4}\right )^2}-4 e^{-x} \left (3-3 x-128 x^3+32 x^4\right )-2 e^{10-\frac {3 x}{2}} \left (6-9 x-256 x^3+96 x^4\right )+e^{5-\frac {5 x}{4}} \left (12-15 x-512 x^3+160 x^4\right )+\frac {e^{15-\frac {3 x}{2}} \left (12-21 x-512 x^3+224 x^4\right )}{e^5+e^{x/4}}\right ) \, dx\\ &=-\left (\frac {1}{8} \int \frac {e^{20-\frac {3 x}{2}} x \left (-3+32 x^3\right )}{\left (e^5+e^{x/4}\right )^2} \, dx\right )+\frac {1}{8} \int e^{5-\frac {5 x}{4}} \left (12-15 x-512 x^3+160 x^4\right ) \, dx+\frac {1}{8} \int \frac {e^{15-\frac {3 x}{2}} \left (12-21 x-512 x^3+224 x^4\right )}{e^5+e^{x/4}} \, dx-\frac {1}{4} \int e^{10-\frac {3 x}{2}} \left (6-9 x-256 x^3+96 x^4\right ) \, dx-\frac {1}{2} \int e^{-x} \left (3-3 x-128 x^3+32 x^4\right ) \, dx\\ &=\frac {1}{8} \int \left (12 e^{5-\frac {5 x}{4}}-15 e^{5-\frac {5 x}{4}} x-512 e^{5-\frac {5 x}{4}} x^3+160 e^{5-\frac {5 x}{4}} x^4\right ) \, dx-\frac {1}{8} \int \left (-\frac {3 e^{20-\frac {3 x}{2}} x}{\left (e^5+e^{x/4}\right )^2}+\frac {32 e^{20-\frac {3 x}{2}} x^4}{\left (e^5+e^{x/4}\right )^2}\right ) \, dx+\frac {1}{8} \int \left (\frac {12 e^{15-\frac {3 x}{2}}}{e^5+e^{x/4}}-\frac {21 e^{15-\frac {3 x}{2}} x}{e^5+e^{x/4}}-\frac {512 e^{15-\frac {3 x}{2}} x^3}{e^5+e^{x/4}}+\frac {224 e^{15-\frac {3 x}{2}} x^4}{e^5+e^{x/4}}\right ) \, dx-\frac {1}{4} \int \left (6 e^{10-\frac {3 x}{2}}-9 e^{10-\frac {3 x}{2}} x-256 e^{10-\frac {3 x}{2}} x^3+96 e^{10-\frac {3 x}{2}} x^4\right ) \, dx-\frac {1}{2} \int \left (3 e^{-x}-3 e^{-x} x-128 e^{-x} x^3+32 e^{-x} x^4\right ) \, dx\\ &=\frac {3}{8} \int \frac {e^{20-\frac {3 x}{2}} x}{\left (e^5+e^{x/4}\right )^2} \, dx-\frac {3}{2} \int e^{10-\frac {3 x}{2}} \, dx+\frac {3}{2} \int e^{5-\frac {5 x}{4}} \, dx-\frac {3}{2} \int e^{-x} \, dx+\frac {3}{2} \int \frac {e^{15-\frac {3 x}{2}}}{e^5+e^{x/4}} \, dx+\frac {3}{2} \int e^{-x} x \, dx-\frac {15}{8} \int e^{5-\frac {5 x}{4}} x \, dx+\frac {9}{4} \int e^{10-\frac {3 x}{2}} x \, dx-\frac {21}{8} \int \frac {e^{15-\frac {3 x}{2}} x}{e^5+e^{x/4}} \, dx-4 \int \frac {e^{20-\frac {3 x}{2}} x^4}{\left (e^5+e^{x/4}\right )^2} \, dx-16 \int e^{-x} x^4 \, dx+20 \int e^{5-\frac {5 x}{4}} x^4 \, dx-24 \int e^{10-\frac {3 x}{2}} x^4 \, dx+28 \int \frac {e^{15-\frac {3 x}{2}} x^4}{e^5+e^{x/4}} \, dx+64 \int e^{10-\frac {3 x}{2}} x^3 \, dx-64 \int e^{5-\frac {5 x}{4}} x^3 \, dx+64 \int e^{-x} x^3 \, dx-64 \int \frac {e^{15-\frac {3 x}{2}} x^3}{e^5+e^{x/4}} \, dx\\ &=e^{10-\frac {3 x}{2}}-\frac {6}{5} e^{5-\frac {5 x}{4}}+\frac {3 e^{-x}}{2}-\frac {3}{2} e^{10-\frac {3 x}{2}} x+\frac {3}{2} e^{5-\frac {5 x}{4}} x-\frac {3 e^{-x} x}{2}-\frac {128}{3} e^{10-\frac {3 x}{2}} x^3+\frac {256}{5} e^{5-\frac {5 x}{4}} x^3-64 e^{-x} x^3+16 e^{10-\frac {3 x}{2}} x^4-16 e^{5-\frac {5 x}{4}} x^4+16 e^{-x} x^4+\frac {3}{8} \int \frac {e^{20-\frac {3 x}{2}} x}{\left (e^5+e^{x/4}\right )^2} \, dx+\frac {3}{2} \int e^{10-\frac {3 x}{2}} \, dx-\frac {3}{2} \int e^{5-\frac {5 x}{4}} \, dx+\frac {3}{2} \int e^{-x} \, dx-\frac {21}{8} \int \frac {e^{15-\frac {3 x}{2}} x}{e^5+e^{x/4}} \, dx-4 \int \frac {e^{20-\frac {3 x}{2}} x^4}{\left (e^5+e^{x/4}\right )^2} \, dx+28 \int \frac {e^{15-\frac {3 x}{2}} x^4}{e^5+e^{x/4}} \, dx-64 \int e^{10-\frac {3 x}{2}} x^3 \, dx+64 \int e^{5-\frac {5 x}{4}} x^3 \, dx-64 \int e^{-x} x^3 \, dx-64 \int \frac {e^{15-\frac {3 x}{2}} x^3}{e^5+e^{x/4}} \, dx+128 \int e^{10-\frac {3 x}{2}} x^2 \, dx-\frac {768}{5} \int e^{5-\frac {5 x}{4}} x^2 \, dx+192 \int e^{-x} x^2 \, dx+\left (6 e^{15}\right ) \operatorname {Subst}\left (\int \frac {1}{x^7 \left (e^5+x\right )} \, dx,x,e^{x/4}\right )\\ &=-\frac {3}{2} e^{10-\frac {3 x}{2}} x+\frac {3}{2} e^{5-\frac {5 x}{4}} x-\frac {3 e^{-x} x}{2}-\frac {256}{3} e^{10-\frac {3 x}{2}} x^2+\frac {3072}{25} e^{5-\frac {5 x}{4}} x^2-192 e^{-x} x^2+16 e^{10-\frac {3 x}{2}} x^4-16 e^{5-\frac {5 x}{4}} x^4+16 e^{-x} x^4+\frac {3}{8} \int \frac {e^{20-\frac {3 x}{2}} x}{\left (e^5+e^{x/4}\right )^2} \, dx-\frac {21}{8} \int \frac {e^{15-\frac {3 x}{2}} x}{e^5+e^{x/4}} \, dx-4 \int \frac {e^{20-\frac {3 x}{2}} x^4}{\left (e^5+e^{x/4}\right )^2} \, dx+28 \int \frac {e^{15-\frac {3 x}{2}} x^4}{e^5+e^{x/4}} \, dx-64 \int \frac {e^{15-\frac {3 x}{2}} x^3}{e^5+e^{x/4}} \, dx-128 \int e^{10-\frac {3 x}{2}} x^2 \, dx+\frac {768}{5} \int e^{5-\frac {5 x}{4}} x^2 \, dx+\frac {512}{3} \int e^{10-\frac {3 x}{2}} x \, dx-192 \int e^{-x} x^2 \, dx-\frac {6144}{25} \int e^{5-\frac {5 x}{4}} x \, dx+384 \int e^{-x} x \, dx+\left (6 e^{15}\right ) \operatorname {Subst}\left (\int \left (\frac {1}{e^5 x^7}-\frac {1}{e^{10} x^6}+\frac {1}{e^{15} x^5}-\frac {1}{e^{20} x^4}+\frac {1}{e^{25} x^3}-\frac {1}{e^{30} x^2}+\frac {1}{e^{35} x}-\frac {1}{e^{35} \left (e^5+x\right )}\right ) \, dx,x,e^{x/4}\right )\\ &=-e^{10-\frac {3 x}{2}}+\frac {6}{5} e^{5-\frac {5 x}{4}}+2 e^{-5-\frac {3 x}{4}}-3 e^{-10-\frac {x}{2}}+6 e^{-15-\frac {x}{4}}-\frac {3 e^{-x}}{2}+\frac {3 x}{2 e^{20}}-\frac {2075}{18} e^{10-\frac {3 x}{2}} x+\frac {49527}{250} e^{5-\frac {5 x}{4}} x-\frac {771 e^{-x} x}{2}+16 e^{10-\frac {3 x}{2}} x^4-16 e^{5-\frac {5 x}{4}} x^4+16 e^{-x} x^4-\frac {6 \log \left (e^5+e^{x/4}\right )}{e^{20}}+\frac {3}{8} \int \frac {e^{20-\frac {3 x}{2}} x}{\left (e^5+e^{x/4}\right )^2} \, dx-\frac {21}{8} \int \frac {e^{15-\frac {3 x}{2}} x}{e^5+e^{x/4}} \, dx-4 \int \frac {e^{20-\frac {3 x}{2}} x^4}{\left (e^5+e^{x/4}\right )^2} \, dx+28 \int \frac {e^{15-\frac {3 x}{2}} x^4}{e^5+e^{x/4}} \, dx-64 \int \frac {e^{15-\frac {3 x}{2}} x^3}{e^5+e^{x/4}} \, dx+\frac {1024}{9} \int e^{10-\frac {3 x}{2}} \, dx-\frac {512}{3} \int e^{10-\frac {3 x}{2}} x \, dx-\frac {24576}{125} \int e^{5-\frac {5 x}{4}} \, dx+\frac {6144}{25} \int e^{5-\frac {5 x}{4}} x \, dx+384 \int e^{-x} \, dx-384 \int e^{-x} x \, dx\\ &=-\frac {2075}{27} e^{10-\frac {3 x}{2}}+\frac {99054}{625} e^{5-\frac {5 x}{4}}+2 e^{-5-\frac {3 x}{4}}-3 e^{-10-\frac {x}{2}}+6 e^{-15-\frac {x}{4}}-\frac {771 e^{-x}}{2}+\frac {3 x}{2 e^{20}}-\frac {3}{2} e^{10-\frac {3 x}{2}} x+\frac {3}{2} e^{5-\frac {5 x}{4}} x-\frac {3 e^{-x} x}{2}+16 e^{10-\frac {3 x}{2}} x^4-16 e^{5-\frac {5 x}{4}} x^4+16 e^{-x} x^4-\frac {6 \log \left (e^5+e^{x/4}\right )}{e^{20}}+\frac {3}{8} \int \frac {e^{20-\frac {3 x}{2}} x}{\left (e^5+e^{x/4}\right )^2} \, dx-\frac {21}{8} \int \frac {e^{15-\frac {3 x}{2}} x}{e^5+e^{x/4}} \, dx-4 \int \frac {e^{20-\frac {3 x}{2}} x^4}{\left (e^5+e^{x/4}\right )^2} \, dx+28 \int \frac {e^{15-\frac {3 x}{2}} x^4}{e^5+e^{x/4}} \, dx-64 \int \frac {e^{15-\frac {3 x}{2}} x^3}{e^5+e^{x/4}} \, dx-\frac {1024}{9} \int e^{10-\frac {3 x}{2}} \, dx+\frac {24576}{125} \int e^{5-\frac {5 x}{4}} \, dx-384 \int e^{-x} \, dx\\ &=-e^{10-\frac {3 x}{2}}+\frac {6}{5} e^{5-\frac {5 x}{4}}+2 e^{-5-\frac {3 x}{4}}-3 e^{-10-\frac {x}{2}}+6 e^{-15-\frac {x}{4}}-\frac {3 e^{-x}}{2}+\frac {3 x}{2 e^{20}}-\frac {3}{2} e^{10-\frac {3 x}{2}} x+\frac {3}{2} e^{5-\frac {5 x}{4}} x-\frac {3 e^{-x} x}{2}+16 e^{10-\frac {3 x}{2}} x^4-16 e^{5-\frac {5 x}{4}} x^4+16 e^{-x} x^4-\frac {6 \log \left (e^5+e^{x/4}\right )}{e^{20}}+\frac {3}{8} \int \frac {e^{20-\frac {3 x}{2}} x}{\left (e^5+e^{x/4}\right )^2} \, dx-\frac {21}{8} \int \frac {e^{15-\frac {3 x}{2}} x}{e^5+e^{x/4}} \, dx-4 \int \frac {e^{20-\frac {3 x}{2}} x^4}{\left (e^5+e^{x/4}\right )^2} \, dx+28 \int \frac {e^{15-\frac {3 x}{2}} x^4}{e^5+e^{x/4}} \, dx-64 \int \frac {e^{15-\frac {3 x}{2}} x^3}{e^5+e^{x/4}} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.40, size = 27, normalized size = 1.00 \begin {gather*} \frac {x \left (-3+32 x^3\right )}{2 \left (e^{5+\frac {3 x}{4}}+e^x\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(-12 + 12*x + 512*x^3 - 128*x^4) + E^((20 + 3*x)/4)*(-12 + 9*x + 512*x^3 - 96*x^4))/(8*E^(2*x)
+ 8*E^((20 + 3*x)/2) + 16*E^(x + (20 + 3*x)/4)),x]

[Out]

(x*(-3 + 32*x^3))/(2*(E^(5 + (3*x)/4) + E^x))

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fricas [A]  time = 0.59, size = 26, normalized size = 0.96 \begin {gather*} \frac {{\left (32 \, x^{4} - 3 \, x\right )} e^{\frac {20}{3}}}{2 \, {\left (e^{\left (x + \frac {20}{3}\right )} + e^{\left (\frac {3}{4} \, x + \frac {35}{3}\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-128*x^4+512*x^3+12*x-12)*exp(x)+(-96*x^4+512*x^3+9*x-12)*exp(3/4*x+5))/(8*exp(x)^2+16*exp(3/4*x+5
)*exp(x)+8*exp(3/4*x+5)^2),x, algorithm="fricas")

[Out]

1/2*(32*x^4 - 3*x)*e^(20/3)/(e^(x + 20/3) + e^(3/4*x + 35/3))

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giac [A]  time = 0.32, size = 22, normalized size = 0.81 \begin {gather*} \frac {32 \, x^{4} - 3 \, x}{2 \, {\left (e^{x} + e^{\left (\frac {3}{4} \, x + 5\right )}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-128*x^4+512*x^3+12*x-12)*exp(x)+(-96*x^4+512*x^3+9*x-12)*exp(3/4*x+5))/(8*exp(x)^2+16*exp(3/4*x+5
)*exp(x)+8*exp(3/4*x+5)^2),x, algorithm="giac")

[Out]

1/2*(32*x^4 - 3*x)/(e^x + e^(3/4*x + 5))

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maple [B]  time = 0.14, size = 71, normalized size = 2.63

method	result	size
risch	\(\frac {x \left (32 x^{3}-3\right ) {\mathrm e}^{-15-\frac {x}{4}}}{2}-\frac {x \left (32 x^{3}-3\right ) {\mathrm e}^{-10-\frac {x}{2}}}{2}+\frac {x \left (32 x^{3}-3\right ) {\mathrm e}^{-5-\frac {3 x}{4}}}{2}-\frac {{\mathrm e}^{-15} x \left (32 x^{3}-3\right )}{2 \left ({\mathrm e}^{5}+{\mathrm e}^{\frac {x}{4}}\right )}\)	\(71\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-128*x^4+512*x^3+12*x-12)*exp(x)+(-96*x^4+512*x^3+9*x-12)*exp(3/4*x+5))/(8*exp(x)^2+16*exp(3/4*x+5)*exp(
x)+8*exp(3/4*x+5)^2),x,method=_RETURNVERBOSE)

[Out]

1/2*x*(32*x^3-3)*exp(-15-1/4*x)-1/2*x*(32*x^3-3)*exp(-10-1/2*x)+1/2*x*(32*x^3-3)*exp(-5-3/4*x)-1/2*exp(-15)*x*
(32*x^3-3)/(exp(5)+exp(1/4*x))

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maxima [B]  time = 0.62, size = 106, normalized size = 3.93 \begin {gather*} 2 \, {\left (3 \, x + 20\right )} e^{\left (-20\right )} - 24 \, e^{\left (-20\right )} \log \left (e^{\frac {20}{3}} + e^{\left (\frac {1}{4} \, x + \frac {5}{3}\right )}\right ) + 24 \, e^{\left (-20\right )} \log \left (e^{5} + e^{\left (\frac {1}{4} \, x\right )}\right ) - \frac {6 \, {\left (x e^{5} + x e^{\left (\frac {1}{4} \, x\right )} + 4 \, e^{5}\right )}}{e^{25} + e^{\left (\frac {1}{4} \, x + 20\right )}} + \frac {2 \, {\left (e^{20} + 12 \, e^{\left (\frac {3}{4} \, x + 5\right )} + 6 \, e^{\left (\frac {1}{2} \, x + 10\right )} - 2 \, e^{\left (\frac {1}{4} \, x + 15\right )}\right )}}{e^{\left (x + 20\right )} + e^{\left (\frac {3}{4} \, x + 25\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-128*x^4+512*x^3+12*x-12)*exp(x)+(-96*x^4+512*x^3+9*x-12)*exp(3/4*x+5))/(8*exp(x)^2+16*exp(3/4*x+5
)*exp(x)+8*exp(3/4*x+5)^2),x, algorithm="maxima")

[Out]

2*(3*x + 20)*e^(-20) - 24*e^(-20)*log(e^(20/3) + e^(1/4*x + 5/3)) + 24*e^(-20)*log(e^5 + e^(1/4*x)) - 6*(x*e^5
+ x*e^(1/4*x) + 4*e^5)/(e^25 + e^(1/4*x + 20)) + 2*(e^20 + 12*e^(3/4*x + 5) + 6*e^(1/2*x + 10) - 2*e^(1/4*x +
15))/(e^(x + 20) + e^(3/4*x + 25))

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mupad [B]  time = 1.13, size = 83, normalized size = 3.07 \begin {gather*} {\mathrm {e}}^{-\frac {x}{2}}\,\left (\frac {3\,x\,{\mathrm {e}}^{-10}}{2}-16\,x^4\,{\mathrm {e}}^{-10}\right )-{\mathrm {e}}^{-\frac {3\,x}{4}}\,\left (\frac {3\,x\,{\mathrm {e}}^{-5}}{2}-16\,x^4\,{\mathrm {e}}^{-5}\right )-{\mathrm {e}}^{-\frac {x}{4}}\,\left (\frac {3\,x\,{\mathrm {e}}^{-15}}{2}-16\,x^4\,{\mathrm {e}}^{-15}\right )+\frac {16\,{\mathrm {e}}^{-15}\,\left (3\,x-32\,x^4\right )}{32\,{\mathrm {e}}^{x/4}+32\,{\mathrm {e}}^5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((3*x)/4 + 5)*(9*x + 512*x^3 - 96*x^4 - 12) + exp(x)*(12*x + 512*x^3 - 128*x^4 - 12))/(8*exp(2*x) + 8*
exp((3*x)/2 + 10) + 16*exp((3*x)/4 + 5)*exp(x)),x)

[Out]

exp(-x/2)*((3*x*exp(-10))/2 - 16*x^4*exp(-10)) - exp(-(3*x)/4)*((3*x*exp(-5))/2 - 16*x^4*exp(-5)) - exp(-x/4)*
((3*x*exp(-15))/2 - 16*x^4*exp(-15)) + (16*exp(-15)*(3*x - 32*x^4))/(32*exp(x/4) + 32*exp(5))

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sympy [B]  time = 0.37, size = 90, normalized size = 3.33 \begin {gather*} \frac {- 32 x^{4} + 3 x}{2 e^{15} e^{\frac {x}{4}} + 2 e^{20}} + \frac {\left (128 x^{4} e^{15} - 12 x e^{15}\right ) e^{- \frac {x}{4}} + \left (- 128 x^{4} e^{20} + 12 x e^{20}\right ) e^{- \frac {x}{2}} + \frac {128 x^{4} e^{25} - 12 x e^{25}}{\left (e^{x}\right )^{\frac {3}{4}}}}{8 e^{30}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-128*x**4+512*x**3+12*x-12)*exp(x)+(-96*x**4+512*x**3+9*x-12)*exp(3/4*x+5))/(8*exp(x)**2+16*exp(3/
4*x+5)*exp(x)+8*exp(3/4*x+5)**2),x)

[Out]

(-32*x**4 + 3*x)/(2*exp(15)*exp(x/4) + 2*exp(20)) + ((128*x**4*exp(15) - 12*x*exp(15))*exp(-x/4) + (-128*x**4*
exp(20) + 12*x*exp(20))*exp(-x/2) + (128*x**4*exp(25) - 12*x*exp(25))/exp(x)**(3/4))*exp(-30)/8

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