- #1

Tanishq Nandan

- 122

- 5

## Homework Statement

Integrate: (sinx + cosx)/sqrt(1+sin2x)

## Homework Equations

Simple trigo formulae:

cos2x=cos^2(x)--sin^2(x)

sin^2(x)+cos^2(x)=1

sin2x=2.sinx.cosx

## The Attempt at a Solution

I tried to rationalize the given term,multiplying both numerator and denominator with:

1st time:cosx-sinx

2nd: sqrt(1-sin2x)

3rd: Both the above terms

Everytime,I only got slightly different terms.

So,went to substitution.

But,I'm not finding any suitable term which I can substitute.

If after rationalizing,I substitute sin2x as a variable,say,T,things might have worked out,

EXCEPT that since I multiplied the term both to numerator and denominator,the other term just makes it impossible to express the whole term in terms of a simple integral.

Any hints? (With or without substitution)