What is the integral of sec^3(t) ?

The integral of sec^3(t) is 1/2 sec(t)tan(t)+1/2 ln|tan(t)+sec(t)|+C

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integral of sec^3(t)

\int sec^{3} (t) d t

\frac{1}{2} sec (t) tan (t) + \frac{1}{2} ln ∣ tan (t) + sec (t) ∣ + C

Solution steps

\int sec^{3} (t) d t

Apply Integral Reduction

= \frac{sec ^{2} ( t ) sin ( t )}{2} + \frac{1}{2} \cdot \int sec (t) d t

\int sec (t) d t = ln ∣ tan (t) + sec (t) ∣

= \frac{sec ^{2} ( t ) sin ( t )}{2} + \frac{1}{2} ln ∣ tan (t) + sec (t) ∣

Simplify

\frac{sec ^{2} ( t ) sin ( t )}{2} + \frac{1}{2} ln ∣ tan (t) + sec (t) ∣ : \frac{1}{2} sec (t) tan (t) + \frac{1}{2} ln ∣ tan (t) + sec (t) ∣

= \frac{1}{2} sec (t) tan (t) + \frac{1}{2} ln ∣ tan (t) + sec (t) ∣

Add a constant to the solution

= \frac{1}{2} sec (t) tan (t) + \frac{1}{2} ln ∣ tan (t) + sec (t) ∣ + C

x \to 2 lim (3 x - 2)

\frac{d}{d x} ((x^{2} + 3)^{2})

\frac{d y}{d x} = \frac{e ^{x - y}}{1 + e ^{x}}, y (1) = 0

\frac{d}{d x} (x^{\frac{1}{11}} (x - 1)^{2})

x \to \infty lim (6^{-})

What is the integral of sec^3(t) ?
The integral of sec^3(t) is 1/2 sec(t)tan(t)+1/2 ln|tan(t)+sec(t)|+C