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

The integral of 1/(1+cos(x)-sin(x)) is -ln|-tan(x/2)+1|+C

Popular >

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

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

- ln - tan (\frac{x}{2}) + 1 + C

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= - ln ∣ v ∣

Substitute back

= - ln - tan (\frac{x}{2}) + 1

Add a constant to the solution

= - ln - tan (\frac{x}{2}) + 1 + C

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

\int x 8 - 2 x^{2} d x

\int \frac{- 2 x + 11}{x ^{2} - 8 x + 25} d x

\int 1 - 2 x^{2} d x

\int (\frac{1}{x + 2}) d x

What is the integral of 1/(1+cos(x)-sin(x)) ?
The integral of 1/(1+cos(x)-sin(x)) is -ln|-tan(x/2)+1|+C