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

The integral of tan(x)sec(x)) is dsec(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of tan(x)sec(x))

\int tan (x) d (sec (x)) d x

d sec (x) + C

Solution steps

\int tan (x) d sec (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= d \cdot \int tan (x) sec (x) d x

Apply u-substitution

: \int 1 d u

= d \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= d \cdot 1 \cdot u

Substitute back

u = sec (x)

= d \cdot 1 \cdot sec (x)

Simplify

= d sec (x)

Add a constant to the solution

= d sec (x) + C

\int \frac{1}{( arctan ( \frac{y}{9} ) ) ( 81 + y ^{2} )} d y

\int (x^{2} - 4)^{3} d x

\int \frac{x - 9}{2 x x} d x

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

What is the integral of tan(x)sec(x)) ?
The integral of tan(x)sec(x)) is dsec(x)+C