To determine

the integral of ∫(cos(lnt)t)dt.

Answer

−sin(lnt)+c.

Explanation

Given:

∫(cos(lnt)t)dt.

∫(cos(lnt)t)dt

Now make the substitution, u=lnt because the differential du=1t×dt occurs.

Thus dtt=du and

∫cos(lnt)tdt=∫cosudu

=sinu+c. (I)

Now substitute the value of u in equation (I) to get:

=−sin(lnt)+c.

Conclusion:

Hence the value of integral is −sin(lnt)+c.