# Trig substitution

1. Mar 8, 2013

### whatlifeforme

1. The problem statement, all variables and given/known data
Use a trigonometric substitution to evaluate the integral.

2. Relevant equations
$\int e^x\,dx$ $/\sqrt{1-e^2x}$

3. The attempt at a solution
e^x = sin∅
x=lnsin∅
dx=cos∅/sin∅

$\frac{sin∅*cos∅}{sin∅*\sqrt{1-(sin∅)^2}}$

$\int sin∅cos∅ / sin∅(cos∅)\,d∅$

$\int \,d∅ = ∅$

e^x = sin∅
∅ = arcsin(e^x)

answer:
∅ + C
arcsin(e^x) + c

Last edited: Mar 8, 2013
2. Mar 8, 2013

### tiny-tim

hi whatlifeforme!
nooo

you forgot the sqrt

(btw it's easier to say ex = sinθ, so exdx = cosθdθ)

3. Mar 8, 2013

### whatlifeforme

so it should be

$\int sin∅cos∅ / sin∅(cos∅)\,dx$

4. Mar 8, 2013

### whatlifeforme

thus,

$\int 1\,d∅$

e^x = sin∅
∅ = arcsin(e^x)

answer: arcsin(e^x) + c

Last edited: Mar 8, 2013
5. Mar 8, 2013

### tiny-tim

yup!

(except of course that integral should have been ∫ 1 dθ )

6. Mar 8, 2013

### whatlifeforme

ooopss. sry fixed.

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