Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

\[\int\frac{- \sin x + 2 \cos x}{2 \sin x + \cos x} dx\]

\[\int\frac{\cos 4x - \cos 2x}{\sin 4x - \sin 2x} dx\]

` ∫ {"cosec"   x }/ { log  tan   x/2 ` dx 

\[\int\frac{1}{      x      \text{log x } \text{log }\left( \text{log x }\right)} dx\]

\[\int\frac{1 - \sin 2x}{x + \cos^2 x} dx\]

\[\int\frac{\sin 2x}{a^2 + b^2 \sin^2 x} dx\]

\[\int\frac{x + 1}{x \left( x + \log x \right)} dx\]

\[\int\frac{1}{\sqrt{1 - x^2}\left( 2 + 3 \sin^{- 1} x \right)} dx\]

\[\int\frac{\sec^2 x}{\tan x + 2} dx\]

\[\int\frac{2 \cos 2x + \sec^2 x}{\sin 2x + \tan x - 5} dx\]

\[\int\frac{\sin 2x}{\sin 5x \sin 3x} dx\]

\[\int\frac{1 + \cot x}{x + \log \sin x} dx\]

` ∫  tan 2x tan 3x  tan 5x    dx  `

\[\int\left\{ 1 + \tan x \tan \left( x + \theta \right) \right\} dx\]

\[\int\frac{\sin 2x}{\sin \left( x - \frac{\pi}{6} \right) \sin \left( x + \frac{\pi}{6} \right)} dx\]

\[\int\frac{\log\left( 1 + \frac{1}{x} \right)}{x \left( 1 + x \right)} dx\]

\[\int\frac{\left( 1 + \sqrt{x} \right)^2}{\sqrt{x}} dx\]

\[\int\sqrt{1 + e^x} .  e^x dx\]

\[\int\frac{\tan x}{\sqrt{\cos x}} dx\]