Evaluate the following integrals : ∫(x+1)e^x/cos^2(xe^x) dx ​

Question

Evaluate the following integrals :

\(\int\frac{(x+1)e^x}{cos^2(xe^x)}\)dx

Answer 1

Assume,

xe^x = t 

d(xe^x) = dt 

(e^x + xe^x) dx = dt 

e^x (1 + x) dx = dt 

Substituting t and dt

⇒ tan t + c 

But,

t = xe^x + 1 

⇒ tan (xe^x) + c.