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

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

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

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

ln ∣ y + sin (y) ∣ + C

Solution steps

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

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 = y + sin (y)

= ln ∣ y + sin (y) ∣

Add a constant to the solution

= ln ∣ y + sin (y) ∣ + C

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