If $\int \frac{x^4}{x-2}dx = px + qx^2 + rx^3 + sx^4 + t\log |x - 2| + C$, where C is an arbitrary constant and p, q, r, s, t are real numbers, then the correct arrangement of p, q, r, s, t is:

$\int e^x \left(\frac{x-1}{2x^2}\right) dx$ is equal to ( where $C$ is an arbitrary constant)

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

$\int_{0}^{\frac{\pi}{2}} \frac{1-\cot x}{\operatorname{cosec} x+\cos x} d x=$

$\int_{-\frac{5}{2}}^{\frac{5}{2}} |x| dx$ is equal to

$\int \frac{2\cos 2x \, dx}{(\sin x+\cos x)^2}$ is equal to:(where C is an arbitrary constant)

$\int 3x^2 e^{x^3}\,dx$ is equal to : (where $C$ is an arbitrary constant)