What is an antiderivative?

Find the antiderivative of f(x) = 4x^3.

A particle's acceleration is given by a(t) = 4t. If the initial velocity is 0, find the velocity function v(t).

Evaluate the integral: $\int \frac{3x^2}{6x^3-4}dx$

Evaluate the integral: $\int \frac{e^{4x}}{9+e^{4x}}dx$