3.60 \(\int \frac{1}{1+t} \, dt\)

Optimal. Leaf size=4 \[ \log (t+1) \]

[Out]

Log[1 + t]

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Rubi [A]  time = 0.00291505, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \log (t+1) \]

Antiderivative was successfully verified.

[In]  Int[(1 + t)^(-1),t]

[Out]

Log[1 + t]

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Rubi in Sympy [A]  time = 0.461584, size = 3, normalized size = 0.75 \[ \log{\left (t + 1 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(1+t),t)

[Out]

log(t + 1)

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Mathematica [A]  time = 0.000867474, size = 4, normalized size = 1. \[ \log (t+1) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 + t)^(-1),t]

[Out]

Log[1 + t]

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Maple [A]  time = 0.002, size = 5, normalized size = 1.3 \[ \ln \left ( 1+t \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1+t),t)

[Out]

ln(1+t)

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Maxima [A]  time = 1.62359, size = 5, normalized size = 1.25 \[ \log \left (t + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(t + 1),t, algorithm="maxima")

[Out]

log(t + 1)

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Fricas [A]  time = 0.191291, size = 5, normalized size = 1.25 \[ \log \left (t + 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(t + 1),t, algorithm="fricas")

[Out]

log(t + 1)

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Sympy [A]  time = 0.026006, size = 3, normalized size = 0.75 \[ \log{\left (t + 1 \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(1+t),t)

[Out]

log(t + 1)

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GIAC/XCAS [A]  time = 0.216236, size = 7, normalized size = 1.75 \[{\rm ln}\left ({\left | t + 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(t + 1),t, algorithm="giac")

[Out]

ln(abs(t + 1))