Mathematics

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


SOLUTION
View Full Answer

Its FREE, you're just one step away


Subjective Hard Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111
Enroll Now For FREE

Realted Questions

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\cfrac { 1 }{ 2\sqrt { 2 } } \tan ^{ -1 }{ \left( \cfrac { 2x-1 }{ \sqrt { 2 } } \right) } +C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
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 $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

View Answer