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

\[\int x \sin x \cos x\ dx\]

` ∫    sin x log  (\text{ cos x ) } dx  `

\[\int \left( \log x \right)^2 \cdot x\ dx\]

\[\int e^\sqrt{x} \text{ dx }\]

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

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

\[\int \log_{10} x\ dx\]

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

\[\int {cosec}^3 x\ dx\]

\[\int \sec^{- 1} \sqrt{x}\ dx\]

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

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

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

\[\int \sin^{- 1} \left( 3x - 4 x^3 \right) \text{ dx }\]

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

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

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

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

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