Mathematics

# Evaluate the given integral.$\displaystyle\int { \cfrac { \log { x } }{ x } } dx$

##### SOLUTION
$I=\displaystyle\int{\dfrac{\log{x}}{x}dx}$

Let $t=\log{x}\Rightarrow\,dt=\dfrac{1}{x}dx$

$=\displaystyle\int{t\,dt}$

$=\dfrac{{t}^{2}}{2}+c$    .........where $c$ is the constant of integration.

$=\dfrac{{\left(\log{x}\right)}^{2}}{2}+c$      ..........where $t=\log{x}$

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int \dfrac{dx}{9x^2 + 1} =$_____.
• A. $\dfrac{1}{3} \tan^{-1} (2x) + c$
• B. $\dfrac{1}{3} \tan^{-1} x + c$
• C. $\dfrac{1}{3} \tan^{-1} (6x) + c$
• D. $\dfrac{1}{3} \tan^{-1} (3x) + c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Integrate the given function $\cfrac{2x}{({x}^{2}+1)({x}^{2}+3)}$=

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Q3 Single Correct Hard
The value of $\displaystyle \sum_{r=1}^{\infty }\tan ^{-1}\frac{2r}{2+r^{2}+r^{4}}$ is equal to
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• B. $\displaystyle \frac{\pi }{2}$
• C. $\displaystyle \pi$
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1 Verified Answer | Published on 17th 09, 2020

Q4 Multiple Correct Hard
If $\displaystyle \int ^{b}_{a}f\left ( t \right )goh\left ( t \right )= \displaystyle \int ^{b}_{a}foh\left ( t \right )\: g\left ( t \right )\: d\left ( t \right )$, where $f, g, h,$ are non negative continuous functions on $\left [ a, b \right ]$ then possible choice of $h\left ( t \right )$ is
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Let $g(x)$ be a function defined on $[0, 7]$ and $g(x)=\int_0^x f(t) dt$, where $y=f(x)$ is the function whose graph is as shown in figure given below, then