Substitution Rule

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June 28th 2010, 03:14 AM
centenial

Substitution Rule

I'm been working problems to help learn the substitution rule for integrals. Is this correct?

$\int\frac{{\sin{\ln{x}}}}{x}dx$

Let $u=\ln{x}$ and $du = \frac{1}{x}dx$ .

$= \int{\sin{u}du}$
$= -\cos{u} + c$
$= -\cos{\ln{x}} + c$

Thanks,
June 28th 2010, 03:29 AM
Chris L T521

Quote:

Originally Posted by centenial

I'm been working problems to help learn the substitution rule for integrals. Is this correct?

$\int\frac{{\sin{\ln{x}}}}{x}dx$

Let $u=\ln{x}$ and $du = \frac{1}{x}dx$ .

$= \int{\sin{u}du}$
$= -\cos{u} + c$
$= -\cos{\ln{x}} + c$

Thanks,

Yes, that's correct.

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