List of top Mathematics Questions on Indefinite Integrals asked in CBSE CLASS XII

If \[ \frac{d}{dx}\bigl(F(x)\bigr)=\frac{1}{e^x+1}, \] then find \(F(x)\), given that the initial condition is \[ F(0)=\log_e\!\left(\frac{1}{2}\right). \]

Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]