CUET Preparation Today
CUET
-- Mathematics - Section B1
Application of Integrals
The integral ∫e−x9+4e−2xdx is equal to
16tan−1(2e−x3)+C
−16tan−1(2e−x3)+C
112tan−1(2e−x3)+C
−112tan−1(2e−x3)+C
I=∫e−x9+4e−2xdx
let y=e−x
dy=−e−xdx⇒−dy=e−xdx
I=−∫dy9+4y2⇒I=−14∫dy(3/2)2+y2
⇒I=−14×23tan−12y3+C
⇒I=−16tan−1(2e−x3)+C