What is the integral of (sin(x)+1)/(cos(x)-x) ?

The integral of (sin(x)+1)/(cos(x)-x) is -ln|cos(x)-x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(x)+1)/(cos(x)-x)

\int \frac{sin ( x ) + 1}{cos ( x ) - x} d x

- ln ∣ cos (x) - x ∣ + C

Solution steps

\int \frac{sin ( x ) + 1}{cos ( x ) - x} d x

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = cos (x) - x

= - ln ∣ cos (x) - x ∣

Add a constant to the solution

= - ln ∣ cos (x) - x ∣ + C

\int \frac{e ^{x}}{e ^{2 x} + 4} d x

\int (3 x + 15)^{15} \cdot 3 d x

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

\int \frac{x ^{3}}{2 x ^{2} + 2} d x

\int sec (2 x) sin (2 x) d x

What is the integral of (sin(x)+1)/(cos(x)-x) ?
The integral of (sin(x)+1)/(cos(x)-x) is -ln|cos(x)-x|+C