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

1 Answer

Jul 28, 2017

# -cos(lnax)+C.#

Explanation:

Suppose that, #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.#

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