Trigonometric substitution for integral with exponential and square root

[annoymage]

Homework Statement

Evaluate $$\int$$$$\frac{e^t}{\sqrt{e^2^t+9}}$$

Homework Equations

N/A

The Attempt at a Solution

i'm using substitution

tan $$\theta$$ = $$\frac{e^t}{3}$$

or i also can use

tan $$\theta$$ = $$\frac{3}{e^t}$$

both will get the same answer.

am i right? because my lecturer told i was wrong, I'm really sure that i did right..
can anyone help me if I am wrong please

 

[tiny-tim]

Hi annoymage!

(never leave out the "dt" after an ∫ )

Both look ok to me.

 

[Cyosis]

It is a possible substitution, but I can't tell you what's wrong until you show your work. That said using a hyperbolic substitution is a lot easier than the one you did.

 

[annoymage]

Hi annoymage!

(never leave out the "dt" after an ∫ )

Both look ok to me.

owho, i forgot the "dt" ;P,

It is a possible substitution, but I can't tell you what's wrong until you show your work. That said using a hyperbolic substitution is a lot easier than the one you did.

i guess this what my lecturer wanted me to do (hyperbolic),

k thanks tiny-tim and cyosis, i fell a lot better now, ahahaa