What is the integral of sec(t)sec(t)+tan(t) ?

The integral of sec(t)sec(t)+tan(t) is tan(t)-ln|cos(t)|+C

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integral of sec(t)sec(t)+tan(t)

\int sec (t) sec (t) + tan (t) d t

tan (t) - ln ∣ cos (t) ∣ + C

Solution steps

\int sec (t) sec (t) + tan (t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int sec (t) sec (t) d t = tan (t)

\int tan (t) d t = - ln ∣ cos (t) ∣

= tan (t) - ln ∣ cos (t) ∣

Add a constant to the solution

= tan (t) - ln ∣ cos (t) ∣ + C

\int_{0}^{\infty} e^{- ∣ x ∣} d x

\frac{d}{d x} ((3 x^{2} - 9)^{- 12})

y = 2^{x}

\int 5 sin^{3} (3 x) cos^{3} (3 x) d x

What is the integral of sec(t)sec(t)+tan(t) ?
The integral of sec(t)sec(t)+tan(t) is tan(t)-ln|cos(t)|+C