Mathematics

# Solve $\int \dfrac { d t } { t ( t + 1 ) }$

##### SOLUTION
$\displaystyle\int{\dfrac{dt}{t\left(t+1\right)}}$

$=\displaystyle\int{\dfrac{\left(t+1-t\right)dt}{t\left(t+1\right)}}$

$=\displaystyle\int{\dfrac{\left(t+1\right)dt}{t\left(t+1\right)}}-\displaystyle\int{\dfrac{tdt}{t\left(t+1\right)}}$

$=\displaystyle\int{\dfrac{dt}{t}}-\displaystyle\int{\dfrac{dt}{\left(t+1\right)}}$

$=\log{\left|t\right|}-\log{\left|t+1\right|}+c$

$=\log{\left|\dfrac{t}{t+1}\right|}+c$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
$\displaystyle \int _{ \dfrac{ 1 }{ e } }^{ e }{ \dfrac { dx }{ x{ \left( \log { x } \right) }^{ \dfrac{ 1 }{ 3 } } } }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\displaystyle\int^{\pi/2}_{\pi/4}\dfrac{(1-3\cos x)}{\sin^2x}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle\int \left(e^x\right)^2 e^x dx$ is equal to

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral :
$\displaystyle\int_{0}^{\pi} ({1+\sin x})\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int \frac{\sin x+\cos x}{\sqrt{\left ( 1+\sin 2x \right )}}$dx is
• A. $\displaystyle \sin x + C$
• B. $\displaystyle \cos x+C$
• C. $\displaystyle \tan x+C$
• D. $x+C$