Integral $I = \displaystyle\int \dfrac{e^{3\log x} - 3x^4}{e^{2\log x} + x^2}\, dx$ (where $x>0$) is equal to

$\int \frac{e^{7\log_e x} - e^{6\log_e x}}{e^{4\log_e x} - e^{3\log_e x}} dx$ is equal to:

(Here, c is an arbitrary constant)

If $g(x) = \int \frac{dx}{x^{1/2} + x^{1/6}}$, then $g(1) - g(0)$ is :

Let $f:\mathbb{R}\to\mathbb{R}$ be a function such that $f(x)+f(y)=f\left(\dfrac{x+y}{1-xy}\right)$, Where $\mathbb{R}$ is set of real numbers then $\alpha+\int_{-\alpha}^{\alpha} f(x)\,dx$ is equal to:

The value of the integral $\int_{-6}^{0} |x+3|\,dx$ is

The integral $\int \frac{dx}{x^2(x^4+1)^{\frac{3}{4}}}$ equals __________.

$\int_{-1}^1 \frac{x^3 + |x| + 1}{x^2 + 2|x| + 1}dx$ is equal to