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

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

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

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

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

Solution steps

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

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

f (x) = \frac{1}{3 x + 2}

\int \frac{9 x ^{2} - 36 x}{4} + 18 d x

\frac{d y}{d x} = cos (x + y)

\frac{\partial}{\partial y} (cos (x) - y)

\int \frac{x ^{4} + 1}{x ^{4} - 1} d x

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