Question

に(1+3)cos r) d equals24·cos (ex(A) - cot (ex) C(C) tan (e*)C(B) tan (xe) + C(D) cot (e C

Answer 1

The given function is e x ( 1+x ) cos 2 ( e x x) .

∫ e x ( 1+x ) cos 2 ( e x x) dx (1)

Let, x e x = t

Now differentiate both the sides,

( x e x + e x .1 )dx=dt e x ( x+1 )dx=dt

Substitute values of t and dt in equation (1).

∫ e ( 1+x ) cos 2 ( e x x) dx = ∫ dt cos 2 t = ∫ sec 2 t =tant+c =tan( e x x)+c

Hence, the integral of the function e x ( 1+x ) cos 2 ( e x x) is tan( e x x)+c, and option B is correct.