It is easy to derive the indefinite integral $$I_1=\int\dfrac{1}{1+\sin x}\,dx~~~~~~~\text{or,}~~~~~~~~~I_2=\int\dfrac{x}{1+\sin x} \, dx$$which are respectively $$I_1=\tan x-\sec x+c_1~~~~~~~\text{and}~~~~~~~~~I_2=x(\tan x-\sec x) + \ln\left|\frac{\sec x+\tan x}{\sec x}\right|+c_2~,$$ where $~c_1,~c_2~$ are independent arbitrary constants. But now
what is the value of the integral $$I_3=\int\dfrac{1}{x+\sin x} \, dx~~ ?$$
N.B. I was trying to solve the problem by using so many methods, but failed to do. Also trying by using online integral calculator. So I need your help.
Sorry to say, please answer the problem (if you have it) rather to make the question closed. I have nothing to provide as additional information.