3.83.22 \(\int \frac {-5 x^3+e^{\frac {4+7 x+2 x^2-x^3+e^{2 x} (-4 x^2+x^3)}{x^2}} (-200-175 x-25 x^3+e^{2 x} (-175 x^3+50 x^4))}{25 e^{\frac {2 (4+7 x+2 x^2-x^3+e^{2 x} (-4 x^2+x^3))}{x^2}} x^3-10 e^{\frac {4+7 x+2 x^2-x^3+e^{2 x} (-4 x^2+x^3)}{x^2}} x^4+x^5} \, dx\)

Optimal. Leaf size=30 \[ \frac {5}{-5 e^{(-4+x) \left (e^{2 x}-\frac {(1+x)^2}{x^2}\right )}+x} \]

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Rubi [F]  time = 31.78, 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 {-5 x^3+\exp \left (\frac {4+7 x+2 x^2-x^3+e^{2 x} \left (-4 x^2+x^3\right )}{x^2}\right ) \left (-200-175 x-25 x^3+e^{2 x} \left (-175 x^3+50 x^4\right )\right )}{25 \exp \left (\frac {2 \left (4+7 x+2 x^2-x^3+e^{2 x} \left (-4 x^2+x^3\right )\right )}{x^2}\right ) x^3-10 \exp \left (\frac {4+7 x+2 x^2-x^3+e^{2 x} \left (-4 x^2+x^3\right )}{x^2}\right ) x^4+x^5} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-5*x^3 + E^((4 + 7*x + 2*x^2 - x^3 + E^(2*x)*(-4*x^2 + x^3))/x^2)*(-200 - 175*x - 25*x^3 + E^(2*x)*(-175*
x^3 + 50*x^4)))/(25*E^((2*(4 + 7*x + 2*x^2 - x^3 + E^(2*x)*(-4*x^2 + x^3)))/x^2)*x^3 - 10*E^((4 + 7*x + 2*x^2
- x^3 + E^(2*x)*(-4*x^2 + x^3))/x^2)*x^4 + x^5),x]

[Out]

-Defer[Int][E^(-2 - E^(2*x)*(-4 + x) - 4/x^2 - 7/x + x), x] - 8*Defer[Int][E^(-2 - E^(2*x)*(-4 + x) - 4/x^2 -
7/x + x)/x^3, x] - 7*Defer[Int][E^(-2 - E^(2*x)*(-4 + x) - 4/x^2 - 7/x + x)/x^2, x] - 5*Defer[Int][E^(2*x)/(5*
E^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) - E^x*x)^2, x] + 250*Defer[Int][E^(4 + 2*E^(2*x)*(-4 + x) + 8/x^2 + 14/
x + 2*x)/(5*E^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) - E^x*x)^2, x] - 875*Defer[Int][E^(4 + 2*E^(2*x)*(-4 + x) +
8/x^2 + 14/x + 2*x)/(x*(5*E^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) - E^x*x)^2), x] - 50*Defer[Int][E^(2 + E^(2*
x)*(-4 + x) + 4/x^2 + 7/x + 2*x)/(5*E^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) - E^x*x), x] + 175*Defer[Int][E^(2
+ E^(2*x)*(-4 + x) + 4/x^2 + 7/x + 2*x)/(x*(5*E^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) - E^x*x)), x] - 40*Defer[
Int][E^(2*x)/(x^2*(-5*E^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) + E^x*x)^2), x] - 35*Defer[Int][E^(2*x)/(x*(-5*E^
(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) + E^x*x)^2), x] - 5*Defer[Int][(E^(2*x)*x)/(-5*E^(2 + E^(2*x)*(-4 + x) +
4/x^2 + 7/x) + E^x*x)^2, x] + 8*Defer[Int][E^(-2 - E^(2*x)*(-4 + x) - 4/x^2 - 7/x + 2*x)/(x^2*(-5*E^(2 + E^(2*
x)*(-4 + x) + 4/x^2 + 7/x) + E^x*x)), x] + 7*Defer[Int][E^(-2 - E^(2*x)*(-4 + x) - 4/x^2 - 7/x + 2*x)/(x*(-5*E
^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) + E^x*x)), x] + Defer[Int][(E^(-2 - E^(2*x)*(-4 + x) - 4/x^2 - 7/x + 2*x
)*x)/(-5*E^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) + E^x*x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2 x} \left (-5 x^3+\exp \left (\frac {4+7 x+2 x^2-x^3+e^{2 x} \left (-4 x^2+x^3\right )}{x^2}\right ) \left (-200-175 x-25 x^3+e^{2 x} \left (-175 x^3+50 x^4\right )\right )\right )}{x^3 \left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )^2} \, dx\\ &=\int \left (-\frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+x} \left (8+7 x+x^3\right )}{x^3}-\frac {5 e^{2 x} \left (8+7 x+175 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}} x+x^2-50 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}} x^2+x^3\right )}{x^2 \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )^2}-\frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+2 x} \left (8+7 x-175 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}} x+50 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}} x^2+x^3\right )}{x^2 \left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )}\right ) \, dx\\ &=-\left (5 \int \frac {e^{2 x} \left (8+7 x+175 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}} x+x^2-50 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}} x^2+x^3\right )}{x^2 \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )^2} \, dx\right )-\int \frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+x} \left (8+7 x+x^3\right )}{x^3} \, dx-\int \frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+2 x} \left (8+7 x-175 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}} x+50 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}} x^2+x^3\right )}{x^2 \left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )} \, dx\\ &=-\left (5 \int \left (\frac {e^{2 x}}{\left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )^2}-\frac {50 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}+2 x}}{\left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )^2}+\frac {175 e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}+2 x}}{x \left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )^2}+\frac {8 e^{2 x}}{x^2 \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )^2}+\frac {7 e^{2 x}}{x \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )^2}+\frac {e^{2 x} x}{\left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )^2}\right ) \, dx\right )-\int \left (e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+x}+\frac {8 e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+x}}{x^3}+\frac {7 e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+x}}{x^2}\right ) \, dx-\int \left (\frac {50 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}+2 x}}{5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x}-\frac {175 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}+2 x}}{x \left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )}-\frac {8 e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+2 x}}{x^2 \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )}-\frac {7 e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+2 x}}{x \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )}-\frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+2 x} x}{-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x}\right ) \, dx\\ &=-\left (5 \int \frac {e^{2 x}}{\left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )^2} \, dx\right )-5 \int \frac {e^{2 x} x}{\left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )^2} \, dx-7 \int \frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+x}}{x^2} \, dx+7 \int \frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+2 x}}{x \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )} \, dx-8 \int \frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+x}}{x^3} \, dx+8 \int \frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+2 x}}{x^2 \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )} \, dx-35 \int \frac {e^{2 x}}{x \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )^2} \, dx-40 \int \frac {e^{2 x}}{x^2 \left (-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x\right )^2} \, dx-50 \int \frac {e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}+2 x}}{5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x} \, dx+175 \int \frac {e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}+2 x}}{x \left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )} \, dx+250 \int \frac {e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}+2 x}}{\left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )^2} \, dx-875 \int \frac {e^{4+2 e^{2 x} (-4+x)+\frac {8}{x^2}+\frac {14}{x}+2 x}}{x \left (5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x\right )^2} \, dx-\int e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+x} \, dx+\int \frac {e^{-2-e^{2 x} (-4+x)-\frac {4}{x^2}-\frac {7}{x}+2 x} x}{-5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}+e^x x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.32, size = 39, normalized size = 1.30 \begin {gather*} -\frac {5 e^x}{5 e^{2+e^{2 x} (-4+x)+\frac {4}{x^2}+\frac {7}{x}}-e^x x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-5*x^3 + E^((4 + 7*x + 2*x^2 - x^3 + E^(2*x)*(-4*x^2 + x^3))/x^2)*(-200 - 175*x - 25*x^3 + E^(2*x)*
(-175*x^3 + 50*x^4)))/(25*E^((2*(4 + 7*x + 2*x^2 - x^3 + E^(2*x)*(-4*x^2 + x^3)))/x^2)*x^3 - 10*E^((4 + 7*x +
2*x^2 - x^3 + E^(2*x)*(-4*x^2 + x^3))/x^2)*x^4 + x^5),x]

[Out]

(-5*E^x)/(5*E^(2 + E^(2*x)*(-4 + x) + 4/x^2 + 7/x) - E^x*x)

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fricas [A]  time = 0.60, size = 42, normalized size = 1.40 \begin {gather*} \frac {5}{x - 5 \, e^{\left (-\frac {x^{3} - 2 \, x^{2} - {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (2 \, x\right )} - 7 \, x - 4}{x^{2}}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((50*x^4-175*x^3)*exp(2*x)-25*x^3-175*x-200)*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)-5*x^3)
/(25*x^3*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)^2-10*x^4*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x
^2)+x^5),x, algorithm="fricas")

[Out]

5/(x - 5*e^(-(x^3 - 2*x^2 - (x^3 - 4*x^2)*e^(2*x) - 7*x - 4)/x^2))

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giac [B]  time = 0.52, size = 1342, normalized size = 44.73 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((50*x^4-175*x^3)*exp(2*x)-25*x^3-175*x-200)*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)-5*x^3)
/(25*x^3*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)^2-10*x^4*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x
^2)+x^5),x, algorithm="giac")

[Out]

5*(2*x^5*e^(4*x) - 7*x^4*e^(4*x) - x^4*e^(2*x) - 10*x^4*e^(4*x + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 +
7*x + 4)/x^2) - x^3*e^(2*x) + 35*x^3*e^(4*x + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) + 5*x
^3*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 7*x^2*e^(2*x) + 5*x^2*e^((x^3*e^(2*x) + x^3
- 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 8*x*e^(2*x) + 35*x*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 +
7*x + 4)/x^2) + 40*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2))/(2*x^6*e^(4*x) - 7*x^5*e^(4*
x) - x^5*e^(2*x) - 10*x^5*e^(4*x + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 10*x^5*e^(2*x
+ (x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - x^4*e^(2*x) + 35*x^4*e^(4*x + (x^3*e^(2*x) - x^
3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) + 50*x^4*e^(2*x + (x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x +
4)/x^2 + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) + 35*x^4*e^(2*x + (x^3*e^(2*x) + x^3 - 4*
x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) + 5*x^4*e^(2*x + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2
) + 5*x^4*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 7*x^3*e^(2*x) - 175*x^3*e^(2*x + (x^
3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2 + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)
/x^2) + 5*x^3*e^(2*x + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 25*x^3*e^((x^3*e^(2*x) + x
^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2 + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) + 5*x^3
*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 8*x^2*e^(2*x) + 35*x^2*e^(2*x + (x^3*e^(2*x)
- x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 25*x^2*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4
)/x^2 + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) + 35*x^2*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2
*x) + 2*x^2 + 7*x + 4)/x^2) + 40*x*e^(2*x + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 175*x
*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2 + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7
*x + 4)/x^2) + 40*x*e^((x^3*e^(2*x) + x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2) - 200*e^((x^3*e^(2*x) + x^3
- 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2 + (x^3*e^(2*x) - x^3 - 4*x^2*e^(2*x) + 2*x^2 + 7*x + 4)/x^2))

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maple [A]  time = 0.26, size = 35, normalized size = 1.17

method	result	size
risch	\(\frac {5}{x -5 \,{\mathrm e}^{\frac {\left (x -4\right ) \left ({\mathrm e}^{2 x} x^{2}-x^{2}-2 x -1\right )}{x^{2}}}}\)	\(35\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((50*x^4-175*x^3)*exp(2*x)-25*x^3-175*x-200)*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)-5*x^3)/(25*x
^3*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)^2-10*x^4*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)+x^
5),x,method=_RETURNVERBOSE)

[Out]

5/(x-5*exp((x-4)*(exp(2*x)*x^2-x^2-2*x-1)/x^2))

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maxima [A]  time = 0.48, size = 46, normalized size = 1.53 \begin {gather*} \frac {5 \, e^{\left (x + 4 \, e^{\left (2 \, x\right )}\right )}}{x e^{\left (x + 4 \, e^{\left (2 \, x\right )}\right )} - 5 \, e^{\left (x e^{\left (2 \, x\right )} + \frac {7}{x} + \frac {4}{x^{2}} + 2\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((50*x^4-175*x^3)*exp(2*x)-25*x^3-175*x-200)*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)-5*x^3)
/(25*x^3*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x^2)^2-10*x^4*exp(((x^3-4*x^2)*exp(2*x)-x^3+2*x^2+7*x+4)/x
^2)+x^5),x, algorithm="maxima")

[Out]

5*e^(x + 4*e^(2*x))/(x*e^(x + 4*e^(2*x)) - 5*e^(x*e^(2*x) + 7/x + 4/x^2 + 2))

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mupad [B]  time = 5.21, size = 40, normalized size = 1.33 \begin {gather*} \frac {5}{x-5\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{x\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{\frac {4}{x^2}}\,{\mathrm {e}}^{7/x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(5*x^3 + exp((7*x - exp(2*x)*(4*x^2 - x^3) + 2*x^2 - x^3 + 4)/x^2)*(175*x + exp(2*x)*(175*x^3 - 50*x^4) +
25*x^3 + 200))/(x^5 - 10*x^4*exp((7*x - exp(2*x)*(4*x^2 - x^3) + 2*x^2 - x^3 + 4)/x^2) + 25*x^3*exp((2*(7*x -
exp(2*x)*(4*x^2 - x^3) + 2*x^2 - x^3 + 4))/x^2)),x)

[Out]

5/(x - 5*exp(-4*exp(2*x))*exp(-x)*exp(2)*exp(x*exp(2*x))*exp(4/x^2)*exp(7/x))

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sympy [A]  time = 0.32, size = 37, normalized size = 1.23 \begin {gather*} - \frac {1}{- \frac {x}{5} + e^{\frac {- x^{3} + 2 x^{2} + 7 x + \left (x^{3} - 4 x^{2}\right ) e^{2 x} + 4}{x^{2}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((50*x**4-175*x**3)*exp(2*x)-25*x**3-175*x-200)*exp(((x**3-4*x**2)*exp(2*x)-x**3+2*x**2+7*x+4)/x**2
)-5*x**3)/(25*x**3*exp(((x**3-4*x**2)*exp(2*x)-x**3+2*x**2+7*x+4)/x**2)**2-10*x**4*exp(((x**3-4*x**2)*exp(2*x)
-x**3+2*x**2+7*x+4)/x**2)+x**5),x)

[Out]

-1/(-x/5 + exp((-x**3 + 2*x**2 + 7*x + (x**3 - 4*x**2)*exp(2*x) + 4)/x**2))

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