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

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

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

\[\int x \sin^5 x^2 \cos x^2 dx\]

\[\int \sin^3 x \cos^4 x\ \text{ dx }\]

\[\int \sin^5 x\ dx\]

\[\int \cos^5 x\ dx\]

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

\[\int\frac{\sin 2x}{\sin^4 x + \cos^4 x} \text{ dx }\]

\[\int\frac{1}{\sqrt{x^2 - a^2}} \text{ dx }\]

\[\int\frac{1}{\sqrt{x^2 + a^2}} \text{ dx }\]

\[\int\frac{1}{4 x^2 + 4x + 5} dx\]

\[\int\frac{1}{x^2 + 4x - 5} \text{ dx }\]

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

\[\int\frac{1}{3 x^2 + 13x - 10} \text{ dx }\]

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

\[\int\sqrt{\text{ cosec  x} - 1} \text{ dx }\]

\[\int\frac{1}{\sqrt{3 - 2x - x^2}} \text{ dx}\]

\[\int\frac{x + 1}{x^2 + 4x + 5} \text{  dx}\]

\[\int\frac{5x + 7}{\sqrt{\left( x - 5 \right) \left( x - 4 \right)}} \text{ dx }\]

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