Question

Integrate the following functions w.r.to ‘x’.

(i) 1/(√(1 - (4x)²)

(ii) 1/√(1 - 81x²)

(iii) 1/(1 + 36x²)

Answer 1

(i) ∫1/(√(1 - (4x)²) dx = (1/4) sin^-1 4x + c

(ii) ∫1/√(1 - 81x²) dx = ∫1/√(1 - (9x)²) dx = (1/9) sin^-1 9x + c

(iii) ∫1/(1 + 36x²) dx = ∫1/(1 + (6x)²) dx = (1/6) tan^-1 6x + c