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

The integral of tan(t)sec(t) is sec(t)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of tan(t)sec(t)

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

sec (t) + C

Solution steps

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

Apply u-substitution

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (t)

= 1 \cdot sec (t)

Simplify

= sec (t)

Add a constant to the solution

= sec (t) + C

\int (2 x - 2 x^{2}) d x

\int \frac{( x + 5 )}{x} d x

\int 3 arcsin (x) d x

\int x y^{2} - cos (x) sin (x) d x

\int \frac{12 x ^{3}}{( 4 x ^{2} + 1 ) ( x - 2 ) ^{2}} d x