PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

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

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

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

\[\int\sqrt{1 + e^x} .  e^x dx\]

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

\[\int\frac{\cos^3 x}{\sqrt{\sin x}} dx\]

\[\int \sin^5\text{ x }\text{cos x dx}\]

\[\int \tan^{3/2} x \sec^2 \text{x dx}\]

\[\int\left( 4x + 2 \right)\sqrt{x^2 + x + 1}  \text{dx}\]

\[\int\frac{1}{1 + \sqrt{x}} dx\]

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

\[\int\frac{\sin 2x}{\left( a + b \cos 2x \right)^2} dx\]

\[\int x^3 \cos x^4 dx\]

\[\int x^3 \sin x^4 dx\]

\[\int\frac{x \sin^{- 1} x^2}{\sqrt{1 - x^4}} dx\]

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

\[\int x^2 e^{x^3} \cos \left( e^{x^3} \right) dx\]

\[\int2x    \sec^3 \left( x^2 + 3 \right) \tan \left( x^2 + 3 \right) dx\]

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