Evaluate the definite integral. (dx)/(1+x^2)

Question

On the integral of tan 4 to tan 9.?

Answer 1

∫(1/1+x²)dx

Substitute formula: ∫(1/1+x²)dx = tan^-1x

= tan^-1x

Substitute the limits [tan4 , tan9]

= tan^-1(tan9) - tan^-1(tan4)

= 9 - 4

= 5

Solution is 5