English

Evaluate ∫1xlogx dx

Advertisements
Advertisements

Question

Evaluate `int 1/(x log x)  "d"x`

Sum
Advertisements

Solution

Let I = `int 1/(x log x)  "d"x`

Put log x = t

∴ `1/x  "d"x` = dt

∴ I = `int1/"t"  "dt"` = log|t| + c

∴ I = log |log x| + c

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.5: Integration - Q.4

RELATED QUESTIONS

If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:

(A) 0

(B) π

(C) π/2

(D) π/4


Integrate the function in x2 log x.


Integrate the function in x tan-1 x.


Integrate the function in (sin-1x)2.


Integrate the function in (x2 + 1) log x.


Integrate the function in `(xe^x)/(1+x)^2`.


`int e^x sec x (1 +   tan x) dx` equals:


Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`


Evaluate the following: `int logx/x.dx`


Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`


Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`


Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`


Choose the correct options from the given alternatives :

`int (log (3x))/(xlog (9x))*dx` =


Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`


Evaluate the following.

`int "e"^"x" "x - 1"/("x + 1")^3` dx


`int ["cosec"(logx)][1 - cot(logx)]  "d"x`


`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`


`int(x + 1/x)^3 dx` = ______.


`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.


Evaluate the following:

`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`


Evaluate the following:

`int_0^1 x log(1 + 2x)  "d"x`


State whether the following statement is true or false.

If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.


Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`


`int(logx)^2dx` equals ______.


`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.


`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.


Solution of the equation `xdy/dx=y log y` is ______


Evaluate the following.

`intx^2e^(4x)dx`


Which substitution can also be used before integrating by parts for \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx?\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×