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

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

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

\[\int\frac{e^x}{e^{2x} + 5 e^x + 6} dx\]

\[\int\frac{e^{3x}}{4 e^{6x} - 9} dx\]

\[\int\frac{dx}{e^x + e^{- x}}\]

\[\int\frac{x}{x^4 + 2 x^2 + 3} dx\]

\[\int\frac{3 x^5}{1 + x^{12}} dx\]

` ∫  { x^2 dx}/{x^6 - a^6} dx `

\[\int\frac{x^2}{x^6 + a^6} dx\]

\[\int\frac{1}{x \left( x^6 + 1 \right)} dx\]

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

\[\int\frac{x}{3 x^4 - 18 x^2 + 11} dx\]

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

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

\[\int\frac{1}{\sqrt{8 + 3x - x^2}} dx\]

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

\[\int\frac{1}{\sqrt{3 x^2 + 5x + 7}} dx\]

\[\int\frac{1}{\sqrt{\left( x - \alpha \right)\left( \beta - x \right)}} dx, \left( \beta > \alpha \right)\]

\[\int\frac{1}{\sqrt{7 - 3x - 2 x^2}} dx\]

\[\int\frac{1}{\sqrt{16 - 6x - x^2}} dx\]