Mathematics

# Find :$\int {\log xdx}$

##### SOLUTION
$\int \log x dx$

Now,
we can also write
$\int \log x\times 1 dx$

it is in from of partial fraction

$\int u\times v=u\int v dx-\int[\dfrac{du}{dx}\times \int v dx]dx$

$=>\log x\int 1dx-\int[\dfrac{d\log x}{dx}\times \int 1 dx]dx$

$=>\log x\times x-\int [\dfrac{1}{x}\times x]dx$

$=>x\log x-\int1dx$
$=>x\log x-x+c$

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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 Hard
Let g be continuous function on R such that $\int g(x)\mathrm{d} x=f(x)+C$, where C is constant of integration. If f(x) is an odd function, $f(1)=3$ and $\int_{-1}^{1}f^{2}(x)g(x)\mathrm{d} x=\lambda$, then $\frac{\lambda }{2}$ is equal to
• A. 10
• B. 11
• C. 12
• D. 9

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Prove that $\displaystyle\int^{\pi/2}_0\dfrac{dx}{(1+\tan x)}=\dfrac{\pi}{4}$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle I = \int \frac {1}{e^x} \tan^{-1} (e^x) dx$, then I equals
• A. $\displaystyle - e^{-x} \tan^{-1} (e^x) + \log (1 + e^{2x}) + C$
• B. $\displaystyle x - e^{-x} \tan^{-1} e^x - \frac {1}{2} \log (1 + e^x) + C$
• C. none of these
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1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
Evaluate $\displaystyle\int \dfrac{(\sin x)^{2018}}{(\cos x)^{2020}}dx$.
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1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Let us consider the integral of the following forms
$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$
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