Question

`int (x + sinx)/(1 + cosx)dx` is equal to ______.

Options

• `x tan  x/2 + C`

• `cot  x/2 + C`

• log(1 + cos x) + C

• log(x + sin x) + C

Answer 1

`int (x + sinx)/(1 + cosx)dx` is equal to `underlinebb(x  tan  x/2 + C)`.

Explanation:

`int (x + sinx)/(1 + cosx)dx = int (x + 2 sin  x/2 cos  x/2)/(2 cos^2  x/2)dx`

= `int[x/2 sec^2  x/2 + tan  x/2]dx`

= `int x 1/2sec^2  x/2dx + int tan  x/2 dx`

= `x tan  x/2 - int tan  x/2 dx + int tan  x/2 dx + C`

= `x tan  x/2 + C`