∫01dxex+e−x
I=∫01dxex+e−x=∫01ex1+e2xdxPut e2=t⇒e2dx=dt∴I=∫e1dt1+t2=[tan−1t]e1=tan−1e−tan−11=tan−1e−π4
If tanθ+secθ=ex, then cosθ equals