Optimal. Leaf size=19 \[ \frac{\text{ExpIntegralEi}(t+1)}{e}-\frac{e^t}{t+1} \]
[Out]
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Rubi [A] time = 0.0398312, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{\text{ExpIntegralEi}(t+1)}{e}-\frac{e^t}{t+1} \]
Antiderivative was successfully verified.
[In] Int[E^t/(1 + t)^2,t]
[Out]
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Rubi in Sympy [A] time = 2.50627, size = 12, normalized size = 0.63 \[ \frac{\operatorname{Ei}{\left (t + 1 \right )}}{e} - \frac{e^{t}}{t + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(t)/(1+t)**2,t)
[Out]
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Mathematica [A] time = 0.011402, size = 19, normalized size = 1. \[ \frac{\text{ExpIntegralEi}(t+1)}{e}-\frac{e^t}{t+1} \]
Antiderivative was successfully verified.
[In] Integrate[E^t/(1 + t)^2,t]
[Out]
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Maple [A] time = 0.008, size = 22, normalized size = 1.2 \[ -{\frac{{{\rm e}^{t}}}{1+t}}-{{\rm e}^{-1}}{\it Ei} \left ( 1,-1-t \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(t)/(1+t)^2,t)
[Out]
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Maxima [A] time = 1.43915, size = 22, normalized size = 1.16 \[ -\frac{e^{\left (-1\right )} exp_integral_e\left (2, -t - 1\right )}{t + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^t/(t + 1)^2,t, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20097, size = 31, normalized size = 1.63 \[ \frac{{\left ({\left (t + 1\right )}{\rm Ei}\left (t + 1\right ) - e^{\left (t + 1\right )}\right )} e^{\left (-1\right )}}{t + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^t/(t + 1)^2,t, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(t)/(1+t)**2,t)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \mathit{undef} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^t/(t + 1)^2,t, algorithm="giac")
[Out]