मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

∫logx(logex)2⋅dx = ______. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

`int logx/(log ex)^2*dx` = ______.

पर्याय

  • `x/(1 + log x) + c`

  • x(1 + log x) + c

  • `1/(1 + log x) + c`

  • `1/(1 - log x) + c`

MCQ
रिकाम्या जागा भरा

उत्तर

`int logx/(log ex)^2*dx` = `underlinebb(x/(1 + log x) + c)`.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Indefinite Integration - Miscellaneous Exercise 3 [पृष्ठ १५०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
पाठ 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.17 | पृष्ठ १५०

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Find : `int(x+3)sqrt(3-4x-x^2dx)`


Integrate the functions:

`1/(x(log x)^m),  x > 0, m ne 1`


Integrate the functions:

`x/(9 - 4x^2)`


Integrate the functions:

`(e^(2x) - 1)/(e^(2x) + 1)`


Integrate the functions:

`(e^(2x) -  e^(-2x))/(e^(2x) + e^(-2x))`


Integrate the functions:

`1/(cos^2 x(1-tan x)^2`


Integrate the functions:

`cos sqrt(x)/sqrtx`


Integrate the functions:

`cos x /(sqrt(1+sinx))`


Integrate the functions:

`sin x/(1+ cos x)`


Integrate the functions:

`1/(1 - tan x)`


Evaluate: `int (2y^2)/(y^2 + 4)dx`


\[\int\sqrt{x - x^2} dx\]

\[\int\sqrt{9 - x^2}\text{ dx}\]

Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]


Write a value of\[\int\frac{\cos x}{\sin x \log \sin x} dx\]

 


Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]


Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]


The value of \[\int\frac{1}{x + x \log x} dx\] is


Find : ` int  (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`


Evaluate the following integrals : `int sin x/cos^2x dx`


Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`


Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`


Evaluate the following integrals : `int cos^2x.dx`


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


Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`


Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`


Integrate the following functions w.r.t. x:

`(10x^9  10^x.log10)/(10^x + x^10)`


Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`


Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`


Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`


Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`


Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`


Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`


Choose the correct options from the given alternatives :

`int f x^x (1 + log x)*dx`


Choose the correct options from the given alternatives :

`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =


Evaluate the following.

`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx


Evaluate the following.

`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt


Evaluate the following.

`int 1/(4"x"^2 - 20"x" + 17)` dx


State whether the following statement is True or False.

If `int x  "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.


Evaluate `int (5"x" + 1)^(4/9)` dx


Evaluate: ∫ |x| dx if x < 0


Evaluate: `int sqrt(x^2 - 8x + 7)` dx


`int 1/sqrt((x - 3)(x + 2))` dx = ______.


`int  ("e"^x(x - 1))/(x^2)  "d"x` = ______ 


`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1))  "d"x`


To find the value of `int ((1 + logx))/x` dx the proper substitution is ______


State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`


State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`


`int sin^-1 x`dx = ?


If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.


If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______ 


If f'(x) = `x + 1/x`, then f(x) is ______.


If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.


`int(log(logx) + 1/(logx)^2)dx` = ______.


The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.


The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.


`int cos^3x  dx` = ______.


Evaluate `int(1 + x + x^2/(2!) )dx`


Evaluated the following

`int x^3/ sqrt (1 + x^4 )dx`


Evaluate `int (1+x+x^2/(2!))dx`


Evaluate `int 1/("x"("x" - 1)) "dx"`


Evaluate `int(1 + x + x^2/(2!))dx`


Evaluate `int1/(x(x - 1))dx`


Evaluate:

`int 1/(1 + cosα . cosx)dx`


Evaluate:

`intsqrt(3 + 4x - 4x^2)  dx`


`int (cos4x)/(sin2x + cos2x)dx` = ______.


Evaluate `int(1+x+(x^2)/(2!))dx`


Evaluate the following:

`int x^3/(sqrt(1+x^4))dx`


Evaluate `int 1/(x(x-1))dx`


Evaluate.

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


Evaluate the following.

`intx^3/sqrt(1 + x^4)dx`


If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x). 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×