English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers2580

Textbook Solutions20345

MCQ Online Mock Tests42

Important Solutions22654

Concept Notes & Videos608

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

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

Evaluation of Definite Integrals by Substitution

Is there an error in this question or solution?

Q 1.8 Q 1.7 Q 2.1

Chapter 19: Indefinite Integrals - Exercise 19.01 [Page 4]

APPEARS IN

RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.01 | Q 1.8 | Page 4

Video TutorialsVIEW ALL [1]

view
Video Tutorials For All Subjects
Evaluation of Definite Integrals by Substitution

video tutorial00:18:12

RELATED QUESTIONS

Evaluate: `int (1+logx)/(x(2+logx)(3+logx))dx`

Evaluate : `int1/(3+5cosx)dx`

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`

Evaluate the integral by using substitution.

`int_0^1 x/(x^2 +1)`dx

Evaluate the integral by using substitution.

`int_0^(pi/2) sqrt(sin phi) cos^5 phidphi`

Evaluate the integral by using substitution.

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

Evaluate the integral by using substitution.

`int_0^(pi/2) (sin x)/(1+ cos^2 x) 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 ______.

Evaluate of the following integral:

\[\int 3^x dx\]

Evaluate:

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

Evaluate:

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

Evaluate:

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

Evaluate:

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

Evaluate the following definite integral:

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

Evaluate the following integral:

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

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 each of the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}}dx\]

Evaluate each of the following integral:

\[\int_{- \frac{\pi}{4}}^\frac{\pi}{4} \frac{\tan^2 x}{1 + e^x}dx\]

Evaluate each of the following integral:

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

Evaluate the following integral:

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

Evaluate the following integral:

\[\int_{- 2}^2 \frac{3 x^3 + 2\left| x \right| + 1}{x^2 + \left| x \right| + 1}dx\]

Evaluate

\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]

Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .

Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .

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

Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x" d"x"`.

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

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

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

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

Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.

If `int x^5 cos (x^6)dx = k sin (x^6) + C`, find the value of k.

Notifications