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
Advertisements

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] Standard 12 Maharashtra State Board
पाठ 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.17 | पृष्ठ १५०

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.


 
 

Evaluate :

`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`

 
 

Integrate the functions:

`(sin^(-1) x)/(sqrt(1-x^2))`


`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:


Evaluate : `∫1/(3+2sinx+cosx)dx`


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


\[\int\sqrt{3 + 2x - x^2} \text{ dx}\]

\[\int\sqrt{16 x^2 + 25} \text{ dx}\]

Write a value of

\[\int e^{\text{ log  sin x  }}\text{ cos x}. \text{ dx}\]

Write a value of

\[\int\frac{1 + \log x}{3 + x \log x} \text{ dx }\] .

Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]


\[\text{ If } \int\left( \frac{x - 1}{x^2} \right) e^x dx = f\left( x \right) e^x + C, \text{ then  write  the value of  f}\left( x \right) .\]

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


Integrate the following w.r.t. x:

`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`


Evaluate the following integrals:

`int (cos2x)/sin^2x dx` 


Evaluate the following integral: 

`int(4x + 3)/(2x + 1).dx`


Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`


If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)


Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`


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

`(5 - 3x)(2 - 3x)^(-1/2)`


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


Evaluate the following : `int (1)/(7 + 2x^2).dx`


Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`


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


Evaluate `int (3"x"^2 - 5)^2` dx


`int sqrt(1 + "x"^2) "dx"` =


Evaluate: `int "e"^sqrt"x"` dx


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


If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______


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


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


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


`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.


The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.


`int (f^'(x))/(f(x))dx` = ______ + c.


`int 1/(sinx.cos^2x)dx` = ______.


`int cos^3x  dx` = ______.


Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.


`int secx/(secx - tanx)dx` equals ______.


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


Evaluate the following

`int1/(x^2 +4x-5)dx`


Evaluate the following.

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


Evaluate:

`int sqrt((a - x)/x) dx`


`int "cosec"^4x  dx` = ______.


Evaluate:

`int sin^3x cos^3x  dx`


The value of `int ("d"x)/(sqrt(1 - x))` is ______.


Evaluate the following.

`intx^3/sqrt(1+x^4)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×