Mathematics

Evaluate :
$$\int { \log x } dx$$


SOLUTION
$$\displaystyle\int{\log{x}dx}$$

let $$u=\log{x}$$ $$v=1$$

Integrating by parts,
$$=x\log{x}-\displaystyle\int{x\times\dfrac{1}{x}dx}$$

$$=x\log{x}-\displaystyle\int 1{dx}$$

$$=x\log{x}-x=x\left(\log{x}-1\right)+c$$
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Evaluate: $$\displaystyle \int _{ 0 }^{ 1 }{ { x\left( 1-x \right)  }^{ n } } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
If $$\displaystyle f\left( x \right)=\int { \frac { { x }^{ 2 }dx }{ \left( 1+{ x }^{ 2 } \right) \left( 1+\sqrt { 1+{ x }^{ 2 } }  \right)  }  } $$ and $$f\left( 0 \right) =0$$, then the value of $$f(1)$$ is
  • A. $$\log { \left( 1+\sqrt { 2 }  \right)  } $$
  • B. $$\displaystyle \log { \left( 1+\sqrt { 2 }  \right)  } +\frac { \pi  }{ 2 } $$
  • C. None of these
  • D. $$\displaystyle \log { \left( 1+\sqrt { 2 }  \right)  } -\frac { \pi  }{ 4 } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Hard
Evaluate:
$$\displaystyle\int _{ 0 }^{ \pi /2 }{ \log { \left( \sin { x }  \right) dx }  } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Evaluate $$\displaystyle \int_{1}^{3}(2x^2+5x)dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
$$\underset {n\rightarrow \infty}{lim}\dfrac{1^2+2^2+3^2+.....+n^2}{n^3}=.................$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer