Calculus
posted by CMM on .
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?
Please help with explanations.

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 
Why is it S (ln u) du = ?
What about the sin? And to multiply them are you reciprocating? 
Oh sorry. It should be:
S sin(u) du 
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?