$\int \frac{x^9}{(4x^2+1)^6}\,dx$ is equal to:

[where c is an arbitrary constant]

The value of the integral $\int_{2}^{4} \frac{x}{x^2+1} dx$ is :

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

Value of $\int_2^3 \frac{\sqrt{x}}{\sqrt{x} + \sqrt{5-x}}dx$ is

$\displaystyle\int \dfrac{1+\cos\theta}{1-\cos\theta}\,d\theta =$

$\int \frac{dx}{\sqrt{5 - 4x - x^2}}$ is equal to

$\int \frac{dx}{2\sin^2 x + 5\cos^2 x}$ is equal to