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

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

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

\[\int\frac{e^x \left( x - 4 \right)}{\left( x - 2 \right)^3} \text{ dx }\]

\[\int\sqrt{3 - 2x - 2 x^2} \text{ dx}\]

\[\int x\sqrt{x^4 + 1} \text{ dx}\]

\[\int x^2 \sqrt{a^6 - x^6} \text{ dx}\]

\[\int\frac{\sqrt{16 + \left( \log x \right)^2}}{x} \text{ dx}\]

\[\int\sqrt{2ax - x^2} \text{ dx}\]

\[\int\sqrt{3 - x^2} \text{ dx}\]

\[\int\sqrt{x^2 - 2x} \text{ dx}\]

\[\int\sqrt{2x - x^2} \text{ dx}\]

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

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

\[\int\left( 2x - 5 \right) \sqrt{2 + 3x - x^2} \text{  dx }\]

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

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

\[\int\left( x - 2 \right) \sqrt{2 x^2 - 6x + 5} \text{  dx }\]

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

\[\int\left( 2x + 3 \right) \sqrt{x^2 + 4x + 3} \text{  dx }\]

\[\int\left( 2x - 5 \right) \sqrt{x^2 - 4x + 3} \text{  dx }\]