List of top Mathematics Questions on integral asked in COMEDK UGET

Evaluate: \[ \int \tan^{-1}\left( \sqrt{\frac{1-\sin x}{1+\sin x}} \right)\,dx \]
\[ \int \frac{dx}{x\sqrt{x^2+4}}= \]
\[ \int(\sin^6x+\cos^6x+3\sin^2x\cos^2x)\,dx= \]
\( \int \left(e^{x\log_e 6}\right)e^x dx = \phi(x) + c \) then \( \phi(x) = \)
If \( \int \frac{\sin 2x}{(1+\sin x)(2+\sin x)} \, dx = a \log |1+\sin x| - b \log |2+\sin x| + c \), then the value of \( a \) and \( b \) is __________.
Evaluate the integral:
\[ \int \frac{dx}{x \sqrt{4x^2 - 9}} \]
Evaluate the integral \( \int \frac{e^{\tan^{-1} x}}{1 + x^2} \, dx \)
If \[ \int \frac{\sin x + \cos x}{\sqrt{1 + 2 \sin x \cos x}} \, dx = \varphi(x) + C, \text{ then } \varphi(x) = \]