Find the integral your answer by differentiation.(t + 1)?dt =t31n(t)-(2/t)-(1/2)t^-2Hint:

Answered: (1+ 1)? dt =D t3

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.5: Derivatives Of Logarithmic Functions

Problem 51E

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Question

Find the integral

your answer by differentiation.
(t + 1)?
dt =
t3
1n(t)-(2/t)-(1/2)t^-2
Hint:

Expert Solution

Step 1 : Analysis

Given :

$\int \frac{{(1 + t)}^{2}}{t^{3}} d t$

Step 2 : Simplificaiton

$\begin{array}{rcl} \int \frac{{(1 + t)}^{2}}{t^{3}} d t & = & \int \frac{1 + 2 t + t^{2}}{t^{3}} d t \\ \int \frac{{(1 + t)}^{2}}{t^{3}} d t & = & \int \frac{1}{t^{3}} d t + \int \frac{2 t}{t^{3}} d t + \int \frac{t^{2}}{t^{3}} d t \\ \int \frac{{(1 + t)}^{2}}{t^{3}} d t & = & \int t^{- 3} d t + 2 \int t^{- 2} d t + \int \frac{1}{t} d t \end{array}$

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