English

Evaluate of the Following Integral: ∫ Log X X D X

Advertisements
Advertisements

Question

Evaluate of the following integral:

\[\int \log_x \text{x  dx}\] 
Sum
Advertisements

Solution

\[\int \log_x x dx\]
\[ = \int1 \cdot dx\]
\[ = x + C\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 18: Indefinite Integrals - Exercise 19.01 [Page 4]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 18 Indefinite Integrals
Exercise 19.01 | Q 1.8 | Page 4

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate :`int_0^(pi/2)1/(1+cosx)dx`

 


 

find `∫_2^4 x/(x^2 + 1)dx`

 

Evaluate the integral by using substitution.

`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`


The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.


If `f(x) = int_0^pi t sin  t  dt`, then f' (x) is ______.


Evaluate of the following integral:

\[\int 3^{2 \log_3} {}^x dx\]

Evaluate: 

\[\int\sqrt{\frac{1 + \cos 2x}{2}}dx\]

Evaluate:

\[\int\sqrt{\frac{1 - \cos 2x}{2}}dx\]

Evaluate: 

\[\int\frac{1}{a^x b^x}dx\]

Evaluate:

\[\int\frac{\cos 2x + 2 \sin^2 x}{\sin^2 x}dx\]

Evaluate: 

\[\int\frac{2 \cos^2 x - \cos 2x}{\cos^2 x}dx\]

\[\int\frac{2x}{\left( 2x + 1 \right)^2} dx\]

Evaluate the following definite integral:

\[\int_0^1 \frac{1}{\sqrt{\left( x - 1 \right)\left( 2 - x \right)}}dx\]

Evaluate the following integral:

\[\int\limits_0^3 \left| 3x - 1 \right| dx\]

 


Evaluate the following integral:

\[\int\limits_{- 6}^6 \left| x + 2 \right| dx\]

 


Evaluate the following integral:

\[\int\limits_1^2 \left| x - 3 \right| dx\]

Evaluate the following integral:

\[\int\limits_0^{\pi/2} \left| \cos 2x \right| dx\]

Evaluate the following integral:

\[\int\limits_0^{2\pi} \left| \sin x \right| dx\]

 


Evaluate the following integral:

\[\int\limits_0^4 \left| x - 1 \right| dx\]

Evaluate the following integral:

\[\int\limits_1^4 \left\{ \left| x - 1 \right| + \left| x - 2 \right| + \left| x - 4 \right| \right\} dx\]

 


Evaluate the following integral:

\[\int\limits_0^4 \left( \left| x \right| + \left| x - 2 \right| + \left| x - 4 \right| \right) dx\]

Evaluate each of the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{\sqrt{\tan x}}{\sqrt{\tan x} + \sqrt{\cot x}}dx\]

Evaluate each of the following integral:

\[\int_{- \frac{\pi}{3}}^\frac{\pi}{3} \frac{1}{1 + e^\ tan\ x}dx\]

 


Evaluate each of the following integral:

\[\int_{- \frac{\pi}{2}}^\frac{\pi}{2} \frac{\cos^2 x}{1 + e^x}dx\]

Evaluate the following integral:

\[\int_0^\frac{\pi}{2} \frac{\tan^7 x}{\tan^7 x + \cot^7 x}dx\]

Evaluate the following integral:

\[\int_0^{2\pi} \sin^{100} x \cos^{101} xdx\]

 


Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .


Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .


Evaluate: `int_  e^x ((2+sin2x))/cos^2 x dx`


Evaluate:  `int_-1^2 (|"x"|)/"x"d"x"`.


`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?


`int_0^1 x(1 - x)^5 "dx" =` ______.


`int_0^(pi4) sec^4x  "d"x` = ______.


Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is


Find: `int (dx)/sqrt(3 - 2x - x^2)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×