definite integral

Evaluate the integral from 0 to infinity of X^2/(X^4+2X^2+1) dx

integral

Evaluate the integral from 0 to inf. of [cos(3x)-cos(5x)]/x^2 dx

Integral of a hard polynomial

Suppose that p(z) and q(z) are polynomials with a complex coefficients with the property that deg q(z) is greater than or equal to deg p(z)+2. If C is a positively oriented simple closed contour containing all of the roots of q(z) on its interior, then prove that integral C of p(z)/q(z) dz = 0

Uning the Euler's identity to calculate the root of i

Calculate the square root of i using a direct method and show that using Euler's formula yield the same result.

f(x,y) algebra equation

I am looking for a software package that can solve simple random equations like f(x,y) as an "input" and plot the 3-D results as the "output" using x, y and jx. My object is to view both real and imaginary parts of the graph on one x, y and jx 3-D coordinate system while using y as the independent variable. Complex math software packages are not required for this limited simple task. Please focus in on the equation input and the 3-D plot output.