3.6 \(\int \sec (x) \tan (x) \, dx\)

Optimal. Leaf size=2 \[ \sec (x) \]

[Out]

Sec[x]

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Rubi [A]  time = 0.0115559, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4 \[ \sec (x) \]

Antiderivative was successfully verified.

[In]  Int[Sec[x]*Tan[x],x]

[Out]

Sec[x]

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Rubi in Sympy [A]  time = 0.768284, size = 3, normalized size = 1.5 \[ \frac{1}{\cos{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(sec(x)*tan(x),x)

[Out]

1/cos(x)

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Mathematica [A]  time = 0.00223956, size = 2, normalized size = 1. \[ \sec (x) \]

Antiderivative was successfully verified.

[In]  Integrate[Sec[x]*Tan[x],x]

[Out]

Sec[x]

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Maple [A]  time = 0., size = 3, normalized size = 1.5 \[ \sec \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(sec(x)*tan(x),x)

[Out]

sec(x)

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Maxima [A]  time = 1.341, size = 5, normalized size = 2.5 \[ \frac{1}{\cos \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sec(x)*tan(x),x, algorithm="maxima")

[Out]

1/cos(x)

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Fricas [A]  time = 0.216057, size = 5, normalized size = 2.5 \[ \frac{1}{\cos \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sec(x)*tan(x),x, algorithm="fricas")

[Out]

1/cos(x)

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Sympy [A]  time = 0.04751, size = 3, normalized size = 1.5 \[ \frac{1}{\cos{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sec(x)*tan(x),x)

[Out]

1/cos(x)

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GIAC/XCAS [A]  time = 0.198644, size = 5, normalized size = 2.5 \[ \frac{1}{\cos \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sec(x)*tan(x),x, algorithm="giac")

[Out]

1/cos(x)