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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 -

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

    S (ln u) du = ?
    Try it yourself

  • Calculus -

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

  • Calculus -

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

  • Calculus -

    So I get this:

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

    Is it correct or incorrect?

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