हिंदी

Evaluate ∫1xlogx dx

Advertisements
Advertisements

प्रश्न

Evaluate `int 1/(x log x)  "d"x`

योग
Advertisements

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.5: Integration - Q.4

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Integrate the function in x2 log x.


Integrate the function in tan-1 x.


Integrate the function in x (log x)2.


Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`


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


Integrate the following w.r.t.x : log (x2 + 1)


Integrate the following w.r.t.x : e2x sin x cos x


Evaluate the following.

∫ x log x dx


Choose the correct alternative from the following.

`int (1 - "x")^(-2) "dx"` = 


Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx


Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx


`int 1/(x^2 - "a"^2)  "d"x` = ______ + c


State whether the following statement is True or False:

If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1|  + B log|x – 2|, then A + B = 1


Evaluate `int 1/(x(x - 1))  "d"x`


Evaluate `int (2x + 1)/((x + 1)(x - 2))  "d"x`


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


The value of `int "e"^(5x) (1/x - 1/(5x^2))  "d"x` is ______.


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


Evaluate the following:

`int_0^1 x log(1 + 2x)  "d"x`


`int tan^-1 sqrt(x)  "d"x` is equal to ______.


Find: `int e^x.sin2xdx`


Evaluate :

`int(4x - 6)/(x^2 - 3x + 5)^(3/2)  dx`


Evaluate: 

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


Evaluate:

`inte^x sinx  dx`


Evaluate the following.

`intx^3/sqrt(1+x^4)  dx`


Which pair is listed as Trigonometric in the LIATE rule?


For \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx,\] which functions are chosen as the first function and the second function?


Using \[t=1-x^2,\] what is \[\int \frac{x\,dx}{\sqrt{1-x^2}}?\]


Let \[I=\int e^x\sin x\,dx.\] After applying integration by parts once, which equation is obtained?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×