How Can I Integrate sqrt(2+2sin(x))?

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To integrate sqrt(2+2sin(x)), first rewrite it as sqrt(2)*sqrt(1+sin(x)). A suggested substitution is tan(x/2) = t, which can help simplify the integral. Transforming the integral leads to sqrt(2) times the integral of sqrt(1+sin(x)) dx. Further manipulation using trigonometric identities, such as expressing sqrt(1+sin(x)) in terms of cos(x), may also assist in solving the integral. The discussion emphasizes the importance of variable substitution and trigonometric transformations in integration.
lostinhere
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I'm having trouble with this. Can anyone help me integrate

sqrt(2+2sin(x))

??

Thanks
 
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lostinhere said:
sqrt(2+2sin(x))
Can you out it into a different form first?

The Bob (2004 ©)
 
Other than
sqrt(2)*sqrt(1+sin(x))

I'm stuck
 
HINT:Make the substitution

\tan\frac{x}{2}=t

Daniel.
 
Can you be more specific please?
 
Transform the integral (make a change of variable).

\sqrt{2}\int \sqrt{1+\sin x} \ dx

x=2\arctan t

Daniel.
 
hello there

sqrt[1+sinx]=[(cosx)^2]/[sqrt[1-sinx]]

see what you could do with that if it helps

steven
 

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