English

Evaluate: ∫ E Log √ X X D X

Advertisements
Advertisements

Question

Evaluate:

\[\int\frac{e\log \sqrt{x}}{x}dx\]
Sum
Advertisements

Solution

\[\int\frac{e\log\sqrt{x}}{x}dx\]
\[ = \int\frac{\sqrt{x}}{x}dx\]
\[ = \int\frac{1}{\sqrt{x}} dx\]
\[ = \int x^{- \frac{1}{2}} dx\]
\[ = \left[ \frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} \right] + C\]
\[ = 2\sqrt{x} + C\]

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 6 | Page 4

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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

 


Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`


 

find `∫_2^4 x/(x^2 + 1)dx`

 

If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.


Evaluate :

`int_e^(e^2) dx/(xlogx)`


Evaluate the integral by using substitution.

`int_0^1 sin^(-1) ((2x)/(1+ x^2)) 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: 

\[\int\frac{1}{x^{3/2}}dx\]

Evaluate of the following integral: 

\[\int 3^x dx\]

Evaluate of the following integral:

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

Evaluate: 

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

Evaluate: 

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

Evaluate the following integral:

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

 


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:

\[\int\limits_{- \pi/2}^{\pi/2} \left\{ \sin \left| x \right| + \cos \left| x \right| \right\} dx\]

 


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:

\[\int_0^{2\pi} \frac{e^\ sin x}{e^\ sin x + e^{- \ sin x}}dx\]

 


Evaluate each of the following integral:

\[\int_{- a}^a \frac{1}{1 + a^x}dx\]`, a > 0`

\[\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}} dx\]

Evaluate the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{1}{1 + \cot^\frac{3}{2} x}dx\]

 


Evaluate the following integral:

\[\int_2^8 \frac{\sqrt{10 - x}}{\sqrt{x} + \sqrt{10 - x}}dx\]

Evaluate the following integral:

\[\int_{- \pi}^\pi \frac{2x\left( 1 + \sin x \right)}{1 + \cos^2 x}dx\]

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


Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.


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


`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.


`int_0^1 sin^-1 ((2x)/(1 + x^2))"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


`int_0^1 x^2e^x dx` = ______.


The value of `int_0^1 (x^4(1 - x)^4)/(1 + x^2) dx` is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×