Question

Evaluate:∫e^(tan^-1)x/1+x^2dx

Answer 1

HELLO DEAR,


GIVEN:-
I = ∫e^tan⁻¹x/(1 + x²) .dx

let t = tan⁻¹x
⇒dt/dx = 1/(1 + x²)
⇒dt = dx/(1 + x²)

∴ I = ∫e^t * dt [ where, t = tan⁻¹x ,dx = dt/(1 + x²)]

⇒I = e^t + c.

⇒I = e^{tan⁻¹x} + c


I HOPE ITS HELP YOU DEAR,
THANKS