Mathematics

# $\displaystyle \int \dfrac{dx}{x\log{x}}$

##### SOLUTION
Let $logx=t$

$\Rightarrow$  $\dfrac{1}{x}dx=dt$

$\Rightarrow$ $\displaystyle \int \dfrac{1}{t}dt$

$\Rightarrow$  $logt+C$

$\Rightarrow$  $log(logx)+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 One Word Medium
Let $\int \frac{dx}{x^{2008} + x} = \frac{1}{p} ln[\frac{x^q}{1 + x^r}] + C$ where p, q, r $\in$ N and need not be distinct, then the sum of the digit in value of (p + q + r) equals

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
$\displaystyle\int \frac{1}{4\sin ^{2}x+9\cos ^{2}x}dx=\frac{1}{k}\tan ^{-1}\left ( \frac{2}{3}\tan x \right ).$ Find the value of $k$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\int x^\cfrac{13}{2} \sqrt{1+x^\cfrac{5}{2}}dx$
• A. $\dfrac{2}{5}(\dfrac{(1+x^\cfrac32)^3}{6}+\dfrac{(1+x^\cfrac52)}{2}-\dfrac{(1+x^\cfrac52)^2}{2})$
• B. $\dfrac{2}{5}(\dfrac{(1+x^\cfrac72)^3}{6}+\dfrac{(1+x^\cfrac52)}{2}-\dfrac{(1+x^\cfrac52)^2}{2})$
• C. $\dfrac{2}{5}(\dfrac{(1+x^\cfrac82)^3}{6}+\dfrac{(1+x^\cfrac52)}{2}-\dfrac{(1+x^\cfrac52)^2}{2})$
• D. $\dfrac{2}{5}(\dfrac{(1+x^\cfrac52)^3}{6}+\dfrac{(1+x^\cfrac52)}{2}-\dfrac{(1+x^\cfrac52)^2}{2})$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate the integrals:
$\displaystyle \int \dfrac{1}{\sqrt{3-4x}}dx$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$