Evaluate ∫ (ex(1+x))/(cos2(xex))dx\(\int\frac{e^x(1+x)}{cos^2(xe^x)

1.	Evaluate ∫ (ex(1+x))/(cos2(xex))dx\(\int\frac{e^x(1+x)}{cos^2(xe^x)}\) dxA. 2 logecos (xex) + C B. sec(xex) + C C. tan(xex) + C D. tan(x + ex) +C
Answer» Option : (C) Given, ∫ (e^x(1+x))/(cos²(xe^x))dx Let (t) = xe^x \(\frac{dt}{dx}\)= e^x(1 + x) ⇒ \(\int\frac{dt}{(cos\,t)^2}\) = \(\int\) (sec t)² dt = tan t (put (t) = x ) = tan (xe^x) + c

Evaluate ∫ (ex(1+x))/(cos2(xex))dx\(\int\frac{e^x(1+x)}{cos^2(xe^x)}\) dxA. 2 logecos (xex) + C B. sec(xex) + C C. tan(xex) + C D. tan(x + ex) +C

Answer»

Option : (C)

Given,

∫ (e^x(1+x))/(cos²(xe^x))dx

Let (t) = xe^x

\(\frac{dt}{dx}\)= e^x(1 + x)

⇒ \(\int\frac{dt}{(cos\,t)^2}\) = \(\int\) (sec t)² dt

= tan t

(put (t) = x )

= tan (xe^x) + c