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

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

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

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

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

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

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

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

\[\int x^3 \tan^{- 1}\text{  x dx }\]

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

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

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

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

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

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

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

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

\[\int\frac{x^3 \sin^{- 1} x^2}{\sqrt{1 - x^4}} \text{ dx }\]

\[\int e^x \left( \tan x - \log \cos x \right) dx\]

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