# Calculus

posted by CMM

Evaluate the integral.
S= integral sign
I= absolute value

S ((cos x)/(2 + sin x))dx

Not sure if I'm doing this right:

u= 2 + sin x
du= 0 + cos x dx

= S du/u = ln IuI + C
= ln I 2 + sin x I + C
= ln (2 + sin x) + C

Another problem:

S ((sin (ln x))/(x)) dx

I don't even know what to put as u and du?

1. agrin04

The first problem is correct.
As for the second problem, take:
u = ln x
du = (1/x) dx

So:
S (ln u) du = ?
Try it yourself

2. CMM

Why is it S (ln u) du = ?
What about the sin? And to multiply them are you reciprocating?

3. agrin04

Oh sorry. It should be:
S sin(u) du

4. CMM

So I get this:

= ln Isin(u)I + C
= ln Isin(ln x)I + C
= ln (sin(ln x)) + C
OR
= ln (sin(1/x)) + C

Is it correct or incorrect?

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