Mathematics

# Solve $\int\cot x \log \sin xdx$

##### SOLUTION
$\int\cot x \log \sin xdx$
Put, $\log \sin x = t$

$\implies \dfrac{1}{\sin x} \cos x dx = dt$

$\implies \cot x dx = dt$

Now, $\int \cot x \log \sin xdx = \int t dt$

$= \dfrac{t^2}{2} + c$

$= \dfrac{(\log \sin x)^2 }{2}+ c$

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

#### Realted Questions

Q1 Single Correct Medium
Solve $\displaystyle \int { { x }^{ 2 }.\sin {2 x }\ dx }$
• A. $\dfrac { { x }^{ 2 }\cos { 2x } }{ 2 } +\dfrac { 2x\sin { 2x } }{ 4 } +\dfrac { 2\cos { 2x } }{ 8 } +c$
• B. $\dfrac { -{ x }^{ 2 }\cos { 2x } }{ 2 } -\dfrac { x\sin { 2x } }{ 2 } +\dfrac { \sin{ 2x } }{ 8 } +c$
• C. $None$
• D. $\dfrac { {- x }^{ 2 }\cos { 2x } }{ 2 } +\dfrac { 2x\sin { 2x } }{ 4 } +\dfrac { 2\cos { 2x } }{ 8 } +c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\int x\cdot log (x+1) dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate : $\displaystyle\int^2_1|x^2-3x+2|dx$
• A. $\dfrac{-1}{6}$
• B. $\dfrac{1}{3}$
• C. $\dfrac{2}{3}$
• D. $\dfrac{1}{6}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate:
$\displaystyle \int _{0}^\dfrac {\pi}{2}{}(2\log \sin x-\log \sin 2x)dx$

If $\displaystyle \int \left[\left(\dfrac{x}{e}\right)^x + \left(\dfrac{e}{x} \right)^x \right] \ln x \, dx = A \left(\dfrac{x}{e}\right)^x + B \left(\dfrac{e}{x} \right)^x + C$, then value of $A + B =$?