3.21.23 \(\int \frac {150-x+e^{4-3 x^2+x^4} (-150+x+900 x^2-600 x^4)+(-50+e^{4-3 x^2+x^4} (50-300 x^2+200 x^4)) \log (-x+e^{4-3 x^2+x^4} x)}{-x+e^{4-3 x^2+x^4} x} \, dx\)

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

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Rubi [F]  time = 9.39, 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 {150-x+e^{4-3 x^2+x^4} \left (-150+x+900 x^2-600 x^4\right )+\left (-50+e^{4-3 x^2+x^4} \left (50-300 x^2+200 x^4\right )\right ) \log \left (-x+e^{4-3 x^2+x^4} x\right )}{-x+e^{4-3 x^2+x^4} x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(150 - x + E^(4 - 3*x^2 + x^4)*(-150 + x + 900*x^2 - 600*x^4) + (-50 + E^(4 - 3*x^2 + x^4)*(50 - 300*x^2 +
200*x^4))*Log[-x + E^(4 - 3*x^2 + x^4)*x])/(-x + E^(4 - 3*x^2 + x^4)*x),x]

[Out]

x + 525*x^2 - (775*x^4)/2 + 150*x^6 - 25*x^8 - 150*Log[x] - 150*x^2*Log[-x + E^(4 - 3*x^2 + x^4)*x] + 50*x^4*L
og[-x + E^(4 - 3*x^2 + x^4)*x] + 50*Defer[Int][Log[-x + E^(4 - 3*x^2 + x^4)*x]/x, x] - 150*Defer[Int][Defer[Su
bst][Defer[Int][E^(3*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2]/x, x] + 900*Defer[Int][x*Defer[Subst][Defer[Int][
E^(3*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2], x] - 900*Defer[Int][(E^(3*x^2)*x*Defer[Subst][Defer[Int][E^(3*x)
/(E^(3*x) - E^(4 + x^2)), x], x, x^2])/(E^(3*x^2) - E^(4 + x^4)), x] - 600*Defer[Int][x^3*Defer[Subst][Defer[I
nt][E^(3*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2], x] + 600*Defer[Int][(E^(3*x^2)*x^3*Defer[Subst][Defer[Int][E
^(3*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2])/(E^(3*x^2) - E^(4 + x^4)), x] + 100*Defer[Int][Defer[Subst][Defer
[Int][(E^(3*x)*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2]/x, x] - 600*Defer[Int][x*Defer[Subst][Defer[Int][(E^(3*
x)*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2], x] + 600*Defer[Int][(E^(3*x^2)*x*Defer[Subst][Defer[Int][(E^(3*x)*
x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2])/(E^(3*x^2) - E^(4 + x^4)), x] + 400*Defer[Int][x^3*Defer[Subst][Defer
[Int][(E^(3*x)*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2], x] - 400*Defer[Int][(E^(3*x^2)*x^3*Defer[Subst][Defer[
Int][(E^(3*x)*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2])/(E^(3*x^2) - E^(4 + x^4)), x] - 450*Defer[Subst][Defer[
Int][E^(3*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2] + 150*Log[-x + E^(4 - 3*x^2 + x^4)*x]*Defer[Subst][Defer[Int
][E^(3*x)/(E^(3*x) - E^(4 + x^2)), x], x, x^2] + 750*Defer[Subst][Defer[Int][(E^(3*x)*x)/(E^(3*x) - E^(4 + x^2
)), x], x, x^2] - 100*Log[-x + E^(4 - 3*x^2 + x^4)*x]*Defer[Subst][Defer[Int][(E^(3*x)*x)/(E^(3*x) - E^(4 + x^
2)), x], x, x^2] - 450*Defer[Subst][Defer[Int][(E^(3*x)*x^2)/(E^(3*x) - E^(4 + x^2)), x], x, x^2] + 100*Defer[
Subst][Defer[Int][(E^(3*x)*x^3)/(E^(3*x) - E^(4 + x^2)), x], x, x^2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {100 e^{3 x^2} x \left (-3+2 x^2\right ) \left (-3+\log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )\right )}{e^{3 x^2}-e^{4+x^4}}+\frac {-150+x+900 x^2-600 x^4+50 \log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )-300 x^2 \log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )+200 x^4 \log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )}{x}\right ) \, dx\\ &=-\left (100 \int \frac {e^{3 x^2} x \left (-3+2 x^2\right ) \left (-3+\log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )\right )}{e^{3 x^2}-e^{4+x^4}} \, dx\right )+\int \frac {-150+x+900 x^2-600 x^4+50 \log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )-300 x^2 \log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )+200 x^4 \log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )}{x} \, dx\\ &=-\left (100 \int \left (-\frac {3 e^{3 x^2} x \left (-3+\log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )\right )}{e^{3 x^2}-e^{4+x^4}}+\frac {2 e^{3 x^2} x^3 \left (-3+\log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )\right )}{e^{3 x^2}-e^{4+x^4}}\right ) \, dx\right )+\int \left (\frac {-150+x+900 x^2-600 x^4}{x}+\frac {50 \left (1-6 x^2+4 x^4\right ) \log \left (-x+e^{4-3 x^2+x^4} x\right )}{x}\right ) \, dx\\ &=50 \int \frac {\left (1-6 x^2+4 x^4\right ) \log \left (-x+e^{4-3 x^2+x^4} x\right )}{x} \, dx-200 \int \frac {e^{3 x^2} x^3 \left (-3+\log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )\right )}{e^{3 x^2}-e^{4+x^4}} \, dx+300 \int \frac {e^{3 x^2} x \left (-3+\log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )\right )}{e^{3 x^2}-e^{4+x^4}} \, dx+\int \frac {-150+x+900 x^2-600 x^4}{x} \, dx\\ &=50 \int \left (\frac {\log \left (-x+e^{4-3 x^2+x^4} x\right )}{x}-6 x \log \left (-x+e^{4-3 x^2+x^4} x\right )+4 x^3 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \, dx-200 \int \left (-\frac {3 e^{3 x^2} x^3}{e^{3 x^2}-e^{4+x^4}}+\frac {e^{3 x^2} x^3 \log \left (-x+e^{4-3 x^2+x^4} x\right )}{e^{3 x^2}-e^{4+x^4}}\right ) \, dx+300 \int \left (-\frac {3 e^{3 x^2} x}{e^{3 x^2}-e^{4+x^4}}+\frac {e^{3 x^2} x \log \left (-x+e^{4-3 x^2+x^4} x\right )}{e^{3 x^2}-e^{4+x^4}}\right ) \, dx+\int \left (1-\frac {150}{x}+900 x-600 x^3\right ) \, dx\\ &=x+450 x^2-150 x^4-150 \log (x)+50 \int \frac {\log \left (-x+e^{4-3 x^2+x^4} x\right )}{x} \, dx+200 \int x^3 \log \left (-x+e^{4-3 x^2+x^4} x\right ) \, dx-200 \int \frac {e^{3 x^2} x^3 \log \left (-x+e^{4-3 x^2+x^4} x\right )}{e^{3 x^2}-e^{4+x^4}} \, dx-300 \int x \log \left (-x+e^{4-3 x^2+x^4} x\right ) \, dx+300 \int \frac {e^{3 x^2} x \log \left (-x+e^{4-3 x^2+x^4} x\right )}{e^{3 x^2}-e^{4+x^4}} \, dx+600 \int \frac {e^{3 x^2} x^3}{e^{3 x^2}-e^{4+x^4}} \, dx-900 \int \frac {e^{3 x^2} x}{e^{3 x^2}-e^{4+x^4}} \, dx\\ &=x+450 x^2-150 x^4-150 \log (x)-150 x^2 \log \left (-x+e^{4-3 x^2+x^4} x\right )+50 x^4 \log \left (-x+e^{4-3 x^2+x^4} x\right )-50 \int \frac {x^3 \left (e^{3 x^2}+e^{4+x^4} \left (-1+6 x^2-4 x^4\right )\right )}{e^{3 x^2}-e^{4+x^4}} \, dx+50 \int \frac {\log \left (-x+e^{4-3 x^2+x^4} x\right )}{x} \, dx+150 \int \frac {x \left (e^{3 x^2}+e^{4+x^4} \left (-1+6 x^2-4 x^4\right )\right )}{e^{3 x^2}-e^{4+x^4}} \, dx+200 \int \frac {\left (e^{3 x^2}+e^{4+x^4} \left (-1+6 x^2-4 x^4\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{2 \left (e^{3 x^2}-e^{4+x^4}\right ) x} \, dx-300 \int \frac {\left (e^{3 x^2}+e^{4+x^4} \left (-1+6 x^2-4 x^4\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{2 \left (e^{3 x^2}-e^{4+x^4}\right ) x} \, dx+300 \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-450 \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-\left (100 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )+\left (150 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )\\ &=x+450 x^2-150 x^4-150 \log (x)-150 x^2 \log \left (-x+e^{4-3 x^2+x^4} x\right )+50 x^4 \log \left (-x+e^{4-3 x^2+x^4} x\right )-25 \operatorname {Subst}\left (\int \frac {x \left (e^{3 x}+e^{4+x^2} \left (-1+6 x-4 x^2\right )\right )}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )+50 \int \frac {\log \left (-x+e^{4-3 x^2+x^4} x\right )}{x} \, dx+75 \operatorname {Subst}\left (\int \frac {e^{3 x}+e^{4+x^2} \left (-1+6 x-4 x^2\right )}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )+100 \int \frac {\left (e^{3 x^2}+e^{4+x^4} \left (-1+6 x^2-4 x^4\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{\left (e^{3 x^2}-e^{4+x^4}\right ) x} \, dx-150 \int \frac {\left (e^{3 x^2}+e^{4+x^4} \left (-1+6 x^2-4 x^4\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{\left (e^{3 x^2}-e^{4+x^4}\right ) x} \, dx+300 \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-450 \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-\left (100 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )+\left (150 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )\\ &=x+450 x^2-150 x^4-150 \log (x)-150 x^2 \log \left (-x+e^{4-3 x^2+x^4} x\right )+50 x^4 \log \left (-x+e^{4-3 x^2+x^4} x\right )-25 \operatorname {Subst}\left (\int \left (-\frac {2 e^{3 x} x^2 (-3+2 x)}{e^{3 x}-e^{4+x^2}}+x \left (1-6 x+4 x^2\right )\right ) \, dx,x,x^2\right )+50 \int \frac {\log \left (-x+e^{4-3 x^2+x^4} x\right )}{x} \, dx+75 \operatorname {Subst}\left (\int \left (1-6 x+4 x^2-\frac {2 e^{3 x} x (-3+2 x)}{e^{3 x}-e^{4+x^2}}\right ) \, dx,x,x^2\right )+100 \int \left (-\frac {2 e^{3 x^2} x \left (-3+2 x^2\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{e^{3 x^2}-e^{4+x^4}}+\frac {\left (1-6 x^2+4 x^4\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{x}\right ) \, dx-150 \int \left (-\frac {2 e^{3 x^2} x \left (-3+2 x^2\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{e^{3 x^2}-e^{4+x^4}}+\frac {\left (1-6 x^2+4 x^4\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{x}\right ) \, dx+300 \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-450 \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-\left (100 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )+\left (150 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )\\ &=x+525 x^2-375 x^4+100 x^6-150 \log (x)-150 x^2 \log \left (-x+e^{4-3 x^2+x^4} x\right )+50 x^4 \log \left (-x+e^{4-3 x^2+x^4} x\right )-25 \operatorname {Subst}\left (\int x \left (1-6 x+4 x^2\right ) \, dx,x,x^2\right )+50 \int \frac {\log \left (-x+e^{4-3 x^2+x^4} x\right )}{x} \, dx+50 \operatorname {Subst}\left (\int \frac {e^{3 x} x^2 (-3+2 x)}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )+100 \int \frac {\left (1-6 x^2+4 x^4\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{x} \, dx-150 \int \frac {\left (1-6 x^2+4 x^4\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{x} \, dx-150 \operatorname {Subst}\left (\int \frac {e^{3 x} x (-3+2 x)}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-200 \int \frac {e^{3 x^2} x \left (-3+2 x^2\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{e^{3 x^2}-e^{4+x^4}} \, dx+300 \int \frac {e^{3 x^2} x \left (-3+2 x^2\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )}{e^{3 x^2}-e^{4+x^4}} \, dx+300 \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-450 \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )-\left (100 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x} x}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )+\left (150 \log \left (-x+e^{4-3 x^2+x^4} x\right )\right ) \operatorname {Subst}\left (\int \frac {e^{3 x}}{e^{3 x}-e^{4+x^2}} \, dx,x,x^2\right )\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.19, size = 174, normalized size = 5.80 \begin {gather*} x+450 x^2-225 x^4+25 \log ^2\left (\left (e^{3 x^2}-e^{4+x^4}\right ) x\right )-150 x^2 \log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )+50 \log \left (e^{3 x^2}-e^{4+x^4}\right ) \left (-3+3 x^2-\log \left (\left (e^{3 x^2}-e^{4+x^4}\right ) x\right )+\log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )\right )+50 \log (x) \left (-3+3 x^2-\log \left (\left (e^{3 x^2}-e^{4+x^4}\right ) x\right )+\log \left (\left (-1+e^{4-3 x^2+x^4}\right ) x\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(150 - x + E^(4 - 3*x^2 + x^4)*(-150 + x + 900*x^2 - 600*x^4) + (-50 + E^(4 - 3*x^2 + x^4)*(50 - 300
*x^2 + 200*x^4))*Log[-x + E^(4 - 3*x^2 + x^4)*x])/(-x + E^(4 - 3*x^2 + x^4)*x),x]

[Out]

x + 450*x^2 - 225*x^4 + 25*Log[(E^(3*x^2) - E^(4 + x^4))*x]^2 - 150*x^2*Log[(-1 + E^(4 - 3*x^2 + x^4))*x] + 50
*Log[E^(3*x^2) - E^(4 + x^4)]*(-3 + 3*x^2 - Log[(E^(3*x^2) - E^(4 + x^4))*x] + Log[(-1 + E^(4 - 3*x^2 + x^4))*
x]) + 50*Log[x]*(-3 + 3*x^2 - Log[(E^(3*x^2) - E^(4 + x^4))*x] + Log[(-1 + E^(4 - 3*x^2 + x^4))*x])

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fricas [A]  time = 0.70, size = 44, normalized size = 1.47 \begin {gather*} 25 \, \log \left (x e^{\left (x^{4} - 3 \, x^{2} + 4\right )} - x\right )^{2} + x - 150 \, \log \left (x e^{\left (x^{4} - 3 \, x^{2} + 4\right )} - x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((200*x^4-300*x^2+50)*exp(x^4-3*x^2+4)-50)*log(x*exp(x^4-3*x^2+4)-x)+(-600*x^4+900*x^2+x-150)*exp(x
^4-3*x^2+4)-x+150)/(x*exp(x^4-3*x^2+4)-x),x, algorithm="fricas")

[Out]

25*log(x*e^(x^4 - 3*x^2 + 4) - x)^2 + x - 150*log(x*e^(x^4 - 3*x^2 + 4) - x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (600 \, x^{4} - 900 \, x^{2} - x + 150\right )} e^{\left (x^{4} - 3 \, x^{2} + 4\right )} - 50 \, {\left ({\left (4 \, x^{4} - 6 \, x^{2} + 1\right )} e^{\left (x^{4} - 3 \, x^{2} + 4\right )} - 1\right )} \log \left (x e^{\left (x^{4} - 3 \, x^{2} + 4\right )} - x\right ) + x - 150}{x e^{\left (x^{4} - 3 \, x^{2} + 4\right )} - x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((200*x^4-300*x^2+50)*exp(x^4-3*x^2+4)-50)*log(x*exp(x^4-3*x^2+4)-x)+(-600*x^4+900*x^2+x-150)*exp(x
^4-3*x^2+4)-x+150)/(x*exp(x^4-3*x^2+4)-x),x, algorithm="giac")

[Out]

integrate(-((600*x^4 - 900*x^2 - x + 150)*e^(x^4 - 3*x^2 + 4) - 50*((4*x^4 - 6*x^2 + 1)*e^(x^4 - 3*x^2 + 4) -
1)*log(x*e^(x^4 - 3*x^2 + 4) - x) + x - 150)/(x*e^(x^4 - 3*x^2 + 4) - x), x)

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maple [A]  time = 0.21, size = 45, normalized size = 1.50

method	result	size
norman	\(x +25 \ln \left (x \,{\mathrm e}^{x^{4}-3 x^{2}+4}-x \right )^{2}-150 \ln \relax (x )-150 \ln \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\)	\(45\)
risch	\(25 \ln \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )^{2}+\left (50 \ln \relax (x )-200\right ) \ln \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )+25 \ln \relax (x )^{2}-200+25 i \pi \ln \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{2}-25 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )+25 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{2}+x -150 \ln \relax (x )-25 i \pi \ln \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{3}+100 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )+100 i \pi \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{3}-100 i \pi \,\mathrm {csgn}\left (i \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{2}+25 i \pi \ln \relax (x ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{2}+50 \ln \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )-100 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{2}-25 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{3}+25 i \pi \ln \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )^{2}-25 i \pi \ln \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right ) \mathrm {csgn}\left (i x \left ({\mathrm e}^{x^{4}-3 x^{2}+4}-1\right )\right )\)	\(547\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((200*x^4-300*x^2+50)*exp(x^4-3*x^2+4)-50)*ln(x*exp(x^4-3*x^2+4)-x)+(-600*x^4+900*x^2+x-150)*exp(x^4-3*x^
2+4)-x+150)/(x*exp(x^4-3*x^2+4)-x),x,method=_RETURNVERBOSE)

[Out]

x+25*ln(x*exp(x^4-3*x^2+4)-x)^2-150*ln(x)-150*ln(exp(x^4-3*x^2+4)-1)

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maxima [B]  time = 0.53, size = 76, normalized size = 2.53 \begin {gather*} 225 \, x^{4} + 450 \, x^{2} - 150 \, {\left (x^{2} + 1\right )} \log \relax (x) + 25 \, \log \relax (x)^{2} - 50 \, {\left (3 \, x^{2} - \log \relax (x) + 3\right )} \log \left (e^{\left (x^{4} + 4\right )} - e^{\left (3 \, x^{2}\right )}\right ) + 25 \, \log \left (e^{\left (x^{4} + 4\right )} - e^{\left (3 \, x^{2}\right )}\right )^{2} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((200*x^4-300*x^2+50)*exp(x^4-3*x^2+4)-50)*log(x*exp(x^4-3*x^2+4)-x)+(-600*x^4+900*x^2+x-150)*exp(x
^4-3*x^2+4)-x+150)/(x*exp(x^4-3*x^2+4)-x),x, algorithm="maxima")

[Out]

225*x^4 + 450*x^2 - 150*(x^2 + 1)*log(x) + 25*log(x)^2 - 50*(3*x^2 - log(x) + 3)*log(e^(x^4 + 4) - e^(3*x^2))
+ 25*log(e^(x^4 + 4) - e^(3*x^2))^2 + x

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mupad [B]  time = 1.30, size = 47, normalized size = 1.57 \begin {gather*} 25\,{\ln \left (x\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-3\,x^2}-x\right )}^2+x-150\,\ln \left ({\mathrm {e}}^{x^4}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-3\,x^2}-1\right )-150\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x*exp(x^4 - 3*x^2 + 4) - x)*(exp(x^4 - 3*x^2 + 4)*(200*x^4 - 300*x^2 + 50) - 50) - x + exp(x^4 - 3*x
^2 + 4)*(x + 900*x^2 - 600*x^4 - 150) + 150)/(x - x*exp(x^4 - 3*x^2 + 4)),x)

[Out]

x - 150*log(exp(x^4)*exp(4)*exp(-3*x^2) - 1) - 150*log(x) + 25*log(x*exp(x^4)*exp(4)*exp(-3*x^2) - x)^2

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sympy [A]  time = 0.56, size = 42, normalized size = 1.40 \begin {gather*} x - 150 \log {\relax (x )} + 25 \log {\left (x e^{x^{4} - 3 x^{2} + 4} - x \right )}^{2} - 150 \log {\left (e^{x^{4} - 3 x^{2} + 4} - 1 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((200*x**4-300*x**2+50)*exp(x**4-3*x**2+4)-50)*ln(x*exp(x**4-3*x**2+4)-x)+(-600*x**4+900*x**2+x-150
)*exp(x**4-3*x**2+4)-x+150)/(x*exp(x**4-3*x**2+4)-x),x)

[Out]

x - 150*log(x) + 25*log(x*exp(x**4 - 3*x**2 + 4) - x)**2 - 150*log(exp(x**4 - 3*x**2 + 4) - 1)

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