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

Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]

Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].

Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]

Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]

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

Write a value of\[\int \log_e x\ dx\].

Write a value of\[\int a^x e^x \text{ dx }\]

Write a value of

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

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