I need to know how to integrate this function:(adsbygoogle = window.adsbygoogle || []).push({});

sin(sqrt(x))

I did this:

u = sqrt(x)

du/dx = 1/(2sqrt(x))

S(sin(sqrt(x))dx) = S(sin(u)*dx*du/dx/(2sqrt(x)) = S(Sin(u)/u du)

But then I got stuck: integration by parts won't work, trig substitution is out...

The one thing I did come up with was:

(u/v)' = (u'v - uv')/v^2

S((u/v)') = uv = S((u'v - uv')/v^2)

So I changed

S(sin(u)/u)

to

S(sin(u)*u/u^2 + cos(u)/u^2 - cos(u)/u^2)

= S((sin(u)*u + cos(u))/u^2) - S(cos(u)/u^2)

= cos(u)/u - S(cos(u)/u^2)

But I get the feeling I'm barking up the wrong tree. If I do integration by parts on that integral I'm going to end up with sin(u)/u again!! :grumpy:

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# Integrating trig(sqr)

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