Homework Help: Calculus

Posted by CMM on Tuesday, March 8, 2011 at 10:16pm.

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.

Calculus - agrin04, Tuesday, March 8, 2011 at 10:55pm
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
Calculus - CMM, Tuesday, March 8, 2011 at 11:14pm
Why is it S (ln u) du = ?
What about the sin? And to multiply them are you reciprocating?
Calculus - agrin04, Tuesday, March 8, 2011 at 11:52pm
Oh sorry. It should be:
S sin(u) du
Calculus - CMM, Wednesday, March 9, 2011 at 1:08am
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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