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Expert-verified Found in: Page 363 ### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280 # Evaluate the integral$$\int {\frac{{{\rm{sin(lnt)}}}}{{\rm{t}}}} {\rm{dt}}$$

Evaluation’s successor is $$\frac{{{\rm{sin(lnt)}}}}{{\rm{t}}}{\rm{dt = - cos(lnt) + C}}$$

See the step by step solution

## Step1: Integral differential.

\begin{aligned}{l}\frac{{{\rm{sin(lnt)}}}}{{\rm{t}}}{\rm{dt}}\\{\rm{ = }}\;\;\;{\rm{sin(lnt)}}\frac{{\rm{1}}}{{\rm{t}}}{\rm{dt}}\end{aligned}

On differentiating, we'll use a substitute.

\begin{aligned}{l}{\rm{ = sin(u)du}}\\{\rm{ = - cos(u) + C}}\end{aligned}

## Step2: Restore the original position$${\rm{u = lnt}}$$.

$${\rm{ = - cos(lnt) + C}}$$

Finally, the original integral position is$$\frac{{{\rm{sin(lnt)}}}}{{\rm{t}}}{\rm{dt = - cos(lnt) + C}}$$. ### Want to see more solutions like these? 