What is the integral of (tan(x)+sec(x))/(sec^2(x)) ?

The integral of (tan(x)+sec(x))/(sec^2(x)) is (sin^2(x))/2+sin(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))/(sec^2(x))

\int \frac{tan ( x ) + sec ( x )}{sec ^{2} ( x )} d x

\frac{sin ^{2} ( x )}{2} + sin (x) + C

Solution steps

\int \frac{tan ( x ) + sec ( x )}{sec ^{2} ( x )} d x

Expand

\frac{tan ( x ) + sec ( x )}{sec ^{2} ( x )} : \frac{tan ( x )}{sec ^{2} ( x )} + \frac{1}{sec ( x )}

= \int \frac{tan ( x )}{sec ^{2} ( x )} + \frac{1}{sec ( x )} d x

Apply the Sum Rule:

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

= \int \frac{tan ( x )}{sec ^{2} ( x )} d x + \int \frac{1}{sec ( x )} d x

\int \frac{tan ( x )}{sec ^{2} ( x )} d x = \frac{sin ^{2} ( x )}{2}

\int \frac{1}{sec ( x )} d x = sin (x)

= \frac{sin ^{2} ( x )}{2} + sin (x)

Add a constant to the solution

= \frac{sin ^{2} ( x )}{2} + sin (x) + C

\int sin (\frac{θ}{2}) tan (\frac{θ}{2}) d θ

\int (7 - csc (x) cot (x)) d x

\int \frac{sin ( 2 x )}{y} + x d x

\int \frac{2}{e ^{2 x} + 6} + \frac{1}{e ^{2 x} - 3} d x

\int 2 π cos (n x) d x

What is the integral of (tan(x)+sec(x))/(sec^2(x)) ?
The integral of (tan(x)+sec(x))/(sec^2(x)) is (sin^2(x))/2+sin(x)+C