Mathematics

# Evaluate:$\int { \cfrac { \sec ^{ 2 }{ x } \left( \log { x } \right) }{ x } } dx\quad$

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Subjective Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Subjective Medium
Evaluate the following definite integrals :
$\displaystyle \int _{0}^{\pi /2} \cos^2 x\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\int { \cfrac { dx }{ (4{ x }^{ 2 }-4x+3) } } =$?
• A. $\cfrac { 1 }{ \sqrt { 2 } } \tan ^{ -1 }{ \left( \cfrac { 2x-1 }{ \sqrt { 2 } } \right) } +C$
• B. $-\cfrac { 1 }{ \sqrt { 2 } } \tan ^{ -1 }{ \left( \cfrac { 2x-1 }{ \sqrt { 2 } } \right) } +C$
• C. none of these
• D. $\cfrac { 1 }{ 2\sqrt { 2 } } \tan ^{ -1 }{ \left( \cfrac { 2x-1 }{ \sqrt { 2 } } \right) } +C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate: $\displaystyle \int { \frac { { x }^{ 3 } }{ { (x+1) }^{ 2 } } dx }$

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Medium
Evaluate:$\displaystyle \int_{-1}^{1}\left [ \sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}} \right ]dx$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$