How do you integrate $\int \frac{sin (ln a x)}{x}$ $int sin(lnax)/x$ using substitution?

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Answer 1 · 2017-07-28T16:39:08

$- cos (ln a x) + C .$ $-cos(lnax)+C.$

Suppose that, $I = \int \frac{sin (ln a x)}{x} d x .$ $I=intsin(lnax)/x dx.$

Subst. $lnax=t :. lna+lnx=t :. (0+1/x)dx=dt, i.e.,$

$1/x dx=dt.$

$:. I=intsintdt=-cost=-cos(lnax)+C.$

How do you integrate int sin(lnax)/x∫sin(lnax)xint sin(lnax)/x using substitution?