Convert any square roots, roots of other powers and powers in denominators to standard power functions. The square root of x equals x^(1/2), the cube root of x equals x^(1/3) and so on for the other roots. To move a power from the denominator to the numerator, take the inverse of the power: 1/x^2 = x^-2, for example.
Add one to the power. For int[(x^3)dx], for example, x^3 becomes x^4.
Divide the result by the new power. For example, x^4 becomes (x^4)/4.
Add the constant of integration, usually represented by c, to complete your answer. For example, [(x^4)/4] + c.