Integrals of the Form (ax + b)

Integrals of the Form ∫ f ( ax + b )dx

We know that

It is clear that whenever a constant is added or subtracted with the independent variable x, the fundamental formulae remain the same.

Here, if any constant is multiplied with the independent variable x, then the same fundamental formula can be used after dividing it by the coefficient of x

The above formula can also be derived by using substitution method, which will be studied later.

Example 11.5

Integrate the following with respect to x:

(i) sin(2x + 4) (ii) sec2 (3 + 4x) (iii) cosec( ax + b ) cot( ax + b)

Solution

EXERCISE 11.2

Integrate the following functions with respect to x: