How do you evaluate an integral when you aren't given any integrands?

Question

The question asks for the integral of x^2 * cos(x^3) but gives no integrands. How do you know what area to give when the question doesn't specify any x values???

Answer 1

Indefinite integral.

Integral x^2 * cos(x^3) dx

The method used u-substitution.

Let u = x^3

then du = 3x^2

Integral x^2 * cos(x^3) dx => integral cos(u) du/3 => sin(u)/3 + constant

=> sin(x^3)/3 + constant    , since u = x^3