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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.2: The Law Of Cosines

Problem 40E

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Question

Find each of the givenintegrals. SHOW ALL YOUR STEPS AND DO NOT INTEGRATE IN YOUR CALCULATOR

Expert Solution

Step 1

To evaluate the integral , $\int \frac{\ln t}{\sqrt{t}} d t$

Solution:

The given integral is $\int \frac{\ln t}{\sqrt{t}} d t$

Using by parts in the given integral where $\ln t$ is the first function and $\frac{1}{\sqrt{t}}$ is the second function.

The integral can evaluate as,

$\begin{array}{rcl} \int \frac{l n t}{\sqrt{t}} d t & = & l n t \int \frac{1}{\sqrt{t}} d t - \int (\frac{d [l n t]}{d x} \int \frac{1}{\sqrt{t}} d t) d t \\ = & l n t (2 \sqrt{t}) - \int (\frac{2 \sqrt{t}}{t}) d t \\ = & (l n t) (2 \sqrt{t}) - 2 \int (\frac{1}{\sqrt{t}}) d t \end{array}$

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