# How to change ∅ in term of x? (integration by trigonometry substitution)

1. Oct 5, 2012

### clifftan

the question is ∫dx/ x^2*√(x^2-1)

I use x=a sec ∅ x^2*√(x^2-1)= sec^2∅tan∅ x=sec ∅
dx= sec∅tan∅d∅

so it will become something like this ∫sec∅tan∅d∅/sec^2∅tan∅= ∫1/sec∅d∅=∫cos∅d∅
=sin∅+c
But how can i change this sin in term of x?

2. Oct 5, 2012

### Muphrid

You said $x = a \sec \theta$.

Can you draw a right triangle for which this is true and solve for the lengths of each of the sides?

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