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

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

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

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

ln ∣ x + cos (x) ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x + cos (x)

= ln ∣ x + cos (x) ∣

Add a constant to the solution

= ln ∣ x + cos (x) ∣ + C

x \to + (- 1) lim (x)

\frac{d}{d x} (- \frac{16}{x ^{3}})

y = \frac{3}{x}, y = 12 x, y = \frac{1}{3} x

h \to 0 lim (\frac{( x - h ) - x}{h})

f (x) = sec (- 4 x^{2} - 3 x + 2)

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