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

Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]

Write a value of

Write a value of

Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]

Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]

Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].

Write a value of\[\int e^{ax} \sin\ bx\ dx\]

Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .

Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .

Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]

Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].

Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]

Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]

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

The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is

The value of \[\int\frac{1}{x + x \log x} dx\] is

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