The value of $I = \displaystyle\int (x^3-1)^{1/3}x^5\,dx$ is

$\int_0^1 \frac{dx}{x^2 + x + 1}$

The integral $I = \int \frac{(1+\log_e x)^3}{x} dx$ is equal to

$\int\limits_{\sqrt{log_e 2}}^{\sqrt{log_e 4}} xe^{x^2} dx$ is equal to

The value of the integral $I = \int_0^1 \frac{1}{\sqrt{1+3\sqrt{x}}} dx$ is

If $\int(\sqrt{x+1} + \sqrt{x-1})^2 dx = \alpha x^2 + \beta x\sqrt{x^2-1} + \gamma \log|x+\sqrt{x^2-1}| + C$, then value of $\alpha + \beta - 2\gamma$ is :

$\int_2^5 |x - 3|dx$ equals