3.65.63 \(\int \frac {128 x^2+32 x^3-2 x^5+e^4 (-64 x^2-32 x^3+4 x^4-2 x^5)+e^{14} (32+8 x+e^4 (-16-8 x+x^2))+e^7 (128 x+32 x^2-2 x^4+e^4 (-64 x-32 x^2+4 x^3-x^4))+(-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} (-16-8 x+x^2)+e^7 (-64 x-32 x^2+4 x^3-x^4)) \log (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 (-16-8 x+x^2)}{e^7 x^2+2 x^3})}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} (-16-8 x+x^2)+e^7 (-64 x-32 x^2+4 x^3-x^4)} \, dx\)

Optimal. Leaf size=33 \[ x \left (e^4+\log \left (2-\frac {x}{2+\frac {e^7}{x}}-\frac {(4+x)^2}{x^2}\right )\right ) \]

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Rubi [F]  time = 8.22, 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 {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(128*x^2 + 32*x^3 - 2*x^5 + E^4*(-64*x^2 - 32*x^3 + 4*x^4 - 2*x^5) + E^14*(32 + 8*x + E^4*(-16 - 8*x + x^2
)) + E^7*(128*x + 32*x^2 - 2*x^4 + E^4*(-64*x - 32*x^2 + 4*x^3 - x^4)) + (-64*x^2 - 32*x^3 + 4*x^4 - 2*x^5 + E
^14*(-16 - 8*x + x^2) + E^7*(-64*x - 32*x^2 + 4*x^3 - x^4))*Log[(-32*x - 16*x^2 + 2*x^3 - x^4 + E^7*(-16 - 8*x
+ x^2))/(E^7*x^2 + 2*x^3)])/(-64*x^2 - 32*x^3 + 4*x^4 - 2*x^5 + E^14*(-16 - 8*x + x^2) + E^7*(-64*x - 32*x^2
+ 4*x^3 - x^4)),x]

[Out]

E^4*x - (256*Log[E^7 + 2*x])/E^14 + (32*Log[E^7 + 2*x])/E^7 - E^7*Log[E^7 + 2*x] - (2*(128 - 64*E^4 - 16*E^7 +
16*E^11 + E^18)*Log[E^7 + 2*x])/E^14 + ((256 - 64*E^7 - 4*E^14 - E^21)*Log[E^7 + 2*x])/(2*E^10) + ((1024 - 51
2*E^4 - 128*E^7 + 128*E^11 + 8*E^18 + 2*E^21 + E^25)*Log[E^7 + 2*x])/(2*E^14) + (64*Log[16*E^7 + 8*(4 + E^7)*x
+ (16 - E^7)*x^2 - 2*x^3 + x^4])/E^14 - (8*Log[16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4])/E^7 -
((64 - 16*E^7 - E^14)*Log[16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4])/(2*E^10) - ((128 - 64*E^4 -
16*E^7 + 16*E^11 + E^18)*Log[16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4])/(2*E^14) + x*Log[-((16*E^
7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4)/(x^2*(E^7 + 2*x)))] + 13*Defer[Int][x^2/(-16*E^7 - 8*(4 + E^
7)*x - (16 - E^7)*x^2 + 2*x^3 - x^4), x] + (512*(12 - E^7)*Defer[Int][(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2
- 2*x^3 + x^4)^(-1), x])/E^14 - (64*(12 - E^7)*Defer[Int][(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 +
x^4)^(-1), x])/E^7 - 4*(4 + E^7)*Defer[Int][(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4)^(-1), x] +
4*(4 + 17*E^7)*Defer[Int][(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4)^(-1), x] - (4*(768 - 256*E^
7 + 4*E^14 + E^21)*Defer[Int][(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4)^(-1), x])/E^10 - (8*(153
6 - 768*E^4 - 320*E^7 + 256*E^11 + 16*E^14 - 4*E^18 + 4*E^21 + E^25)*Defer[Int][(16*E^7 + 8*(4 + E^7)*x + (16
- E^7)*x^2 - 2*x^3 + x^4)^(-1), x])/E^14 + (4*(1536 - 768*E^4 - 320*E^7 + 256*E^11 + 16*E^14 - 4*E^18 - 8*E^21
+ 3*E^25)*Defer[Int][(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4)^(-1), x])/E^14 - (48 - E^7)*Defe
r[Int][x/(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4), x] + (128*(16 + E^7)*Defer[Int][x/(16*E^7 +
8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4), x])/E^14 - (16*(16 + E^7)*Defer[Int][x/(16*E^7 + 8*(4 + E^7)*x
+ (16 - E^7)*x^2 - 2*x^3 + x^4), x])/E^7 + (112 + 23*E^7)*Defer[Int][x/(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^
2 - 2*x^3 + x^4), x] - ((1024 - 192*E^7 - E^21)*Defer[Int][x/(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3
+ x^4), x])/E^10 - (2*(2048 - 1024*E^4 - 128*E^7 + 192*E^11 + 48*E^14 + 8*E^21 + 5*E^25)*Defer[Int][x/(16*E^7
+ 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4), x])/E^14 + ((2048 - 1024*E^4 - 128*E^7 + 192*E^11 + 48*E^14 -
8*E^21 + 9*E^25)*Defer[Int][x/(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4), x])/E^14 + (16*Defer[I
nt][x^2/(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4), x])/E^7 + (29 - 2*E^7)*Defer[Int][x^2/(16*E^7
+ 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4), x] - (128*(1 + E^7)*Defer[Int][x^2/(16*E^7 + 8*(4 + E^7)*x +
(16 - E^7)*x^2 - 2*x^3 + x^4), x])/E^14 + ((64 + 48*E^7 - 17*E^14)*Defer[Int][x^2/(16*E^7 + 8*(4 + E^7)*x + (
16 - E^7)*x^2 - 2*x^3 + x^4), x])/E^10 - ((128 - 64*E^4 + 112*E^7 - 48*E^11 - 16*E^14 + 17*E^18 + E^25)*Defer[
Int][x^2/(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4), x])/E^14 + ((256 - 128*E^4 + 224*E^7 - 96*E^
11 - 32*E^14 + 34*E^18 + 2*E^21 + E^25)*Defer[Int][x^2/(16*E^7 + 8*(4 + E^7)*x + (16 - E^7)*x^2 - 2*x^3 + x^4)
, x])/E^14

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {128 x^2}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {32 x^3}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {2 x^5}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {e^{14} \left (-16 \left (2-e^4\right )-8 \left (1-e^4\right ) x-e^4 x^2\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {2 e^4 x^2 \left (32+16 x-2 x^2+x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {e^7 x \left (-64 \left (2-e^4\right )-32 \left (1-e^4\right ) x-4 e^4 x^2+\left (2+e^4\right ) x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\log \left (\frac {-16 e^7-8 \left (4+e^7\right ) x-\left (16-e^7\right ) x^2+2 x^3-x^4}{x^2 \left (e^7+2 x\right )}\right )\right ) \, dx\\ &=2 \int \frac {x^5}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+32 \int \frac {x^3}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+128 \int \frac {x^2}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+\left (2 e^4\right ) \int \frac {x^2 \left (32+16 x-2 x^2+x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+e^7 \int \frac {x \left (-64 \left (2-e^4\right )-32 \left (1-e^4\right ) x-4 e^4 x^2+\left (2+e^4\right ) x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+e^{14} \int \frac {-16 \left (2-e^4\right )-8 \left (1-e^4\right ) x-e^4 x^2}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+\int \log \left (\frac {-16 e^7-8 \left (4+e^7\right ) x-\left (16-e^7\right ) x^2+2 x^3-x^4}{x^2 \left (e^7+2 x\right )}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.27, size = 51, normalized size = 1.55 \begin {gather*} e^4 x+x \log \left (\frac {e^7 \left (-16-8 x+x^2\right )-x \left (32+16 x-2 x^2+x^3\right )}{x^2 \left (e^7+2 x\right )}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(128*x^2 + 32*x^3 - 2*x^5 + E^4*(-64*x^2 - 32*x^3 + 4*x^4 - 2*x^5) + E^14*(32 + 8*x + E^4*(-16 - 8*x
+ x^2)) + E^7*(128*x + 32*x^2 - 2*x^4 + E^4*(-64*x - 32*x^2 + 4*x^3 - x^4)) + (-64*x^2 - 32*x^3 + 4*x^4 - 2*x
^5 + E^14*(-16 - 8*x + x^2) + E^7*(-64*x - 32*x^2 + 4*x^3 - x^4))*Log[(-32*x - 16*x^2 + 2*x^3 - x^4 + E^7*(-16
- 8*x + x^2))/(E^7*x^2 + 2*x^3)])/(-64*x^2 - 32*x^3 + 4*x^4 - 2*x^5 + E^14*(-16 - 8*x + x^2) + E^7*(-64*x - 3
2*x^2 + 4*x^3 - x^4)),x]

[Out]

E^4*x + x*Log[(E^7*(-16 - 8*x + x^2) - x*(32 + 16*x - 2*x^2 + x^3))/(x^2*(E^7 + 2*x))]

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fricas [A]  time = 0.99, size = 53, normalized size = 1.61 \begin {gather*} x e^{4} + x \log \left (-\frac {x^{4} - 2 \, x^{3} + 16 \, x^{2} - {\left (x^{2} - 8 \, x - 16\right )} e^{7} + 32 \, x}{2 \, x^{3} + x^{2} e^{7}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-8*x-16)*exp(7)^2+(-x^4+4*x^3-32*x^2-64*x)*exp(7)-2*x^5+4*x^4-32*x^3-64*x^2)*log(((x^2-8*x-16)
*exp(7)-x^4+2*x^3-16*x^2-32*x)/(x^2*exp(7)+2*x^3))+((x^2-8*x-16)*exp(4)+8*x+32)*exp(7)^2+((-x^4+4*x^3-32*x^2-6
4*x)*exp(4)-2*x^4+32*x^2+128*x)*exp(7)+(-2*x^5+4*x^4-32*x^3-64*x^2)*exp(4)-2*x^5+32*x^3+128*x^2)/((x^2-8*x-16)
*exp(7)^2+(-x^4+4*x^3-32*x^2-64*x)*exp(7)-2*x^5+4*x^4-32*x^3-64*x^2),x, algorithm="fricas")

[Out]

x*e^4 + x*log(-(x^4 - 2*x^3 + 16*x^2 - (x^2 - 8*x - 16)*e^7 + 32*x)/(2*x^3 + x^2*e^7))

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giac [A]  time = 2.17, size = 57, normalized size = 1.73 \begin {gather*} x e^{4} + x \log \left (-\frac {x^{4} - 2 \, x^{3} - x^{2} e^{7} + 16 \, x^{2} + 8 \, x e^{7} + 32 \, x + 16 \, e^{7}}{2 \, x^{3} + x^{2} e^{7}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-8*x-16)*exp(7)^2+(-x^4+4*x^3-32*x^2-64*x)*exp(7)-2*x^5+4*x^4-32*x^3-64*x^2)*log(((x^2-8*x-16)
*exp(7)-x^4+2*x^3-16*x^2-32*x)/(x^2*exp(7)+2*x^3))+((x^2-8*x-16)*exp(4)+8*x+32)*exp(7)^2+((-x^4+4*x^3-32*x^2-6
4*x)*exp(4)-2*x^4+32*x^2+128*x)*exp(7)+(-2*x^5+4*x^4-32*x^3-64*x^2)*exp(4)-2*x^5+32*x^3+128*x^2)/((x^2-8*x-16)
*exp(7)^2+(-x^4+4*x^3-32*x^2-64*x)*exp(7)-2*x^5+4*x^4-32*x^3-64*x^2),x, algorithm="giac")

[Out]

x*e^4 + x*log(-(x^4 - 2*x^3 - x^2*e^7 + 16*x^2 + 8*x*e^7 + 32*x + 16*e^7)/(2*x^3 + x^2*e^7))

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maple [A]  time = 0.62, size = 54, normalized size = 1.64

method	result	size
norman	\(x \,{\mathrm e}^{4}+x \ln \left (\frac {\left (x^{2}-8 x -16\right ) {\mathrm e}^{7}-x^{4}+2 x^{3}-16 x^{2}-32 x}{x^{2} {\mathrm e}^{7}+2 x^{3}}\right )\)	\(54\)
risch	\(x \,{\mathrm e}^{4}+x \ln \left (\frac {\left (x^{2}-8 x -16\right ) {\mathrm e}^{7}-x^{4}+2 x^{3}-16 x^{2}-32 x}{x^{2} {\mathrm e}^{7}+2 x^{3}}\right )\)	\(54\)
default	\(x \,{\mathrm e}^{4}+\frac {\left (\munderset {\textit {\_R} =\RootOf \left (2 \textit {\_Z}^{5}+\left ({\mathrm e}^{7}-4\right ) \textit {\_Z}^{4}+\left (-4 \,{\mathrm e}^{7}+32\right ) \textit {\_Z}^{3}+\left (32 \,{\mathrm e}^{7}-{\mathrm e}^{14}+64\right ) \textit {\_Z}^{2}+\left (64 \,{\mathrm e}^{7}+8 \,{\mathrm e}^{14}\right ) \textit {\_Z} +16 \,{\mathrm e}^{14}\right )}{\sum }\frac {\left (\left ({\mathrm e}^{7}+4\right ) \textit {\_R}^{4}+4 \left ({\mathrm e}^{7}-16\right ) \textit {\_R}^{3}+\left (-64 \,{\mathrm e}^{7}+{\mathrm e}^{14}-192\right ) \textit {\_R}^{2}+16 \left (-12 \,{\mathrm e}^{7}-{\mathrm e}^{14}\right ) \textit {\_R} -48 \,{\mathrm e}^{14}\right ) \ln \left (x -\textit {\_R} \right )}{2 \textit {\_R}^{3} {\mathrm e}^{7}+5 \textit {\_R}^{4}-6 \textit {\_R}^{2} {\mathrm e}^{7}-8 \textit {\_R}^{3}+32 \textit {\_R} \,{\mathrm e}^{7}-{\mathrm e}^{14} \textit {\_R} +48 \textit {\_R}^{2}+32 \,{\mathrm e}^{7}+4 \,{\mathrm e}^{14}+64 \textit {\_R}}\right )}{2}+x \ln \left (\frac {-x^{4}+x^{2} {\mathrm e}^{7}+2 x^{3}-8 x \,{\mathrm e}^{7}-16 x^{2}-16 \,{\mathrm e}^{7}-32 x}{x^{2} \left ({\mathrm e}^{7}+2 x \right )}\right )+{\mathrm e}^{-28} \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+\left (-{\mathrm e}^{7}+16\right ) \textit {\_Z}^{2}+\left (8 \,{\mathrm e}^{7}+32\right ) \textit {\_Z} +16 \,{\mathrm e}^{7}\right )}{\sum }\frac {\left (\textit {\_R}^{3} {\mathrm e}^{28}+\left (-16 \,{\mathrm e}^{28}+{\mathrm e}^{35}\right ) \textit {\_R}^{2}+12 \left (-4 \,{\mathrm e}^{28}-{\mathrm e}^{35}\right ) \textit {\_R} -32 \,{\mathrm e}^{35}\right ) \ln \left (x -\textit {\_R} \right )}{-16-2 \textit {\_R}^{3}+\textit {\_R} \,{\mathrm e}^{7}+3 \textit {\_R}^{2}-4 \,{\mathrm e}^{7}-16 \textit {\_R}}\right )-\frac {{\mathrm e}^{7} \ln \left ({\mathrm e}^{7}+2 x \right )}{2}+2 \ln \left ({\mathrm e}^{7}+2 x \right )+64 \,{\mathrm e}^{-7} \ln \left ({\mathrm e}^{7}+2 x \right )-2 \,{\mathrm e}^{-14} \ln \left ({\mathrm e}^{7}+2 x \right ) {\mathrm e}^{14}-384 \,{\mathrm e}^{-14} \ln \left ({\mathrm e}^{7}+2 x \right )-64 \,{\mathrm e}^{-21} \ln \left ({\mathrm e}^{7}+2 x \right ) {\mathrm e}^{14}+384 \,{\mathrm e}^{-28} \ln \left ({\mathrm e}^{7}+2 x \right ) {\mathrm e}^{14}\)	\(415\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^2-8*x-16)*exp(7)^2+(-x^4+4*x^3-32*x^2-64*x)*exp(7)-2*x^5+4*x^4-32*x^3-64*x^2)*ln(((x^2-8*x-16)*exp(7)
-x^4+2*x^3-16*x^2-32*x)/(x^2*exp(7)+2*x^3))+((x^2-8*x-16)*exp(4)+8*x+32)*exp(7)^2+((-x^4+4*x^3-32*x^2-64*x)*ex
p(4)-2*x^4+32*x^2+128*x)*exp(7)+(-2*x^5+4*x^4-32*x^3-64*x^2)*exp(4)-2*x^5+32*x^3+128*x^2)/((x^2-8*x-16)*exp(7)
^2+(-x^4+4*x^3-32*x^2-64*x)*exp(7)-2*x^5+4*x^4-32*x^3-64*x^2),x,method=_RETURNVERBOSE)

[Out]

x*exp(4)+x*ln(((x^2-8*x-16)*exp(7)-x^4+2*x^3-16*x^2-32*x)/(x^2*exp(7)+2*x^3))

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maxima [A]  time = 0.40, size = 53, normalized size = 1.61 \begin {gather*} x e^{4} + x \log \left (-x^{4} + 2 \, x^{3} + x^{2} {\left (e^{7} - 16\right )} - 8 \, x {\left (e^{7} + 4\right )} - 16 \, e^{7}\right ) - x \log \left (2 \, x + e^{7}\right ) - 2 \, x \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-8*x-16)*exp(7)^2+(-x^4+4*x^3-32*x^2-64*x)*exp(7)-2*x^5+4*x^4-32*x^3-64*x^2)*log(((x^2-8*x-16)
*exp(7)-x^4+2*x^3-16*x^2-32*x)/(x^2*exp(7)+2*x^3))+((x^2-8*x-16)*exp(4)+8*x+32)*exp(7)^2+((-x^4+4*x^3-32*x^2-6
4*x)*exp(4)-2*x^4+32*x^2+128*x)*exp(7)+(-2*x^5+4*x^4-32*x^3-64*x^2)*exp(4)-2*x^5+32*x^3+128*x^2)/((x^2-8*x-16)
*exp(7)^2+(-x^4+4*x^3-32*x^2-64*x)*exp(7)-2*x^5+4*x^4-32*x^3-64*x^2),x, algorithm="maxima")

[Out]

x*e^4 + x*log(-x^4 + 2*x^3 + x^2*(e^7 - 16) - 8*x*(e^7 + 4) - 16*e^7) - x*log(2*x + e^7) - 2*x*log(x)

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mupad [B]  time = 5.03, size = 52, normalized size = 1.58 \begin {gather*} x\,\left (\ln \left (-\frac {32\,x+{\mathrm {e}}^7\,\left (-x^2+8\,x+16\right )+16\,x^2-2\,x^3+x^4}{2\,x^3+{\mathrm {e}}^7\,x^2}\right )+{\mathrm {e}}^4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(14)*(8*x - exp(4)*(8*x - x^2 + 16) + 32) - log(-(32*x + exp(7)*(8*x - x^2 + 16) + 16*x^2 - 2*x^3 + x
^4)/(x^2*exp(7) + 2*x^3))*(exp(14)*(8*x - x^2 + 16) + exp(7)*(64*x + 32*x^2 - 4*x^3 + x^4) + 64*x^2 + 32*x^3 -
4*x^4 + 2*x^5) + exp(7)*(128*x - exp(4)*(64*x + 32*x^2 - 4*x^3 + x^4) + 32*x^2 - 2*x^4) + 128*x^2 + 32*x^3 -
2*x^5 - exp(4)*(64*x^2 + 32*x^3 - 4*x^4 + 2*x^5))/(exp(14)*(8*x - x^2 + 16) + exp(7)*(64*x + 32*x^2 - 4*x^3 +
x^4) + 64*x^2 + 32*x^3 - 4*x^4 + 2*x^5),x)

[Out]

x*(log(-(32*x + exp(7)*(8*x - x^2 + 16) + 16*x^2 - 2*x^3 + x^4)/(x^2*exp(7) + 2*x^3)) + exp(4))

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sympy [A]  time = 0.58, size = 48, normalized size = 1.45 \begin {gather*} x \log {\left (\frac {- x^{4} + 2 x^{3} - 16 x^{2} - 32 x + \left (x^{2} - 8 x - 16\right ) e^{7}}{2 x^{3} + x^{2} e^{7}} \right )} + x e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**2-8*x-16)*exp(7)**2+(-x**4+4*x**3-32*x**2-64*x)*exp(7)-2*x**5+4*x**4-32*x**3-64*x**2)*ln(((x**
2-8*x-16)*exp(7)-x**4+2*x**3-16*x**2-32*x)/(x**2*exp(7)+2*x**3))+((x**2-8*x-16)*exp(4)+8*x+32)*exp(7)**2+((-x*
*4+4*x**3-32*x**2-64*x)*exp(4)-2*x**4+32*x**2+128*x)*exp(7)+(-2*x**5+4*x**4-32*x**3-64*x**2)*exp(4)-2*x**5+32*
x**3+128*x**2)/((x**2-8*x-16)*exp(7)**2+(-x**4+4*x**3-32*x**2-64*x)*exp(7)-2*x**5+4*x**4-32*x**3-64*x**2),x)

[Out]

x*log((-x**4 + 2*x**3 - 16*x**2 - 32*x + (x**2 - 8*x - 16)*exp(7))/(2*x**3 + x**2*exp(7))) + x*exp(4)

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