$\int e^{2x}(\sin x + \frac{1}{2}\cos x) dx$ is equal to

Value of $\int \left(\frac{1}{logx} - \frac{1}{(logx)^2}\right)dx$ is

The integral $I = \int \frac{(1+\log x)^3}{x}\, dx$ equals:

$\int e^x \left(\frac{1-x}{1+x^2}\right)^2 dx =$

The value of $\int_{0}^{\pi/2} \frac{\tan^7 x}{\cot^7 x + \tan^7 x} dx$ is

$\int \frac{dx}{9x^2 - 16}$ is equal to

The value of the definite integral $I = \int_{1}^{2} \frac{1}{x(1 + x^2)}dx$ is: