English

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

Advertisements
Advertisements

Question

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

Options

  • `x/(1 + log x) + c`

  • x(1 + log x) + c

  • `1/(1 + log x) + c`

  • `1/(1 - log x) + c`

MCQ
Fill in the Blanks

Solution

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Miscellaneous Exercise 3 [Page 150]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.17 | Page 150

RELATED QUESTIONS

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`


Evaluate :`intxlogxdx`


Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Evaluate :

`int(sqrt(cotx)+sqrt(tanx))dx`


Find `intsqrtx/sqrt(a^3-x^3)dx`


Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.


Evaluate: `int sqrt(tanx)/(sinxcosx) dx`


Integrate the functions:

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


Integrate the functions:

`sqrt(ax + b)`


Integrate the functions:

`1/(x(log x)^m),  x > 0, m ne 1`


Integrate the functions:

`1/(1 - tan x)`


Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .

Write a value of\[\int \log_e x\ dx\].

 


Write a value of\[\int e^{ax} \cos\ bx\ dx\].

 


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


Integrate the following w.r.t. x : x3 + x2 – x + 1


Evaluate the following integrals : `int (sin2x)/(cosx)dx`


Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`


Evaluate the following integrals:

`int x/(x + 2).dx`


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


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


Integrate the following functions w.r.t. x : sin4x.cos3x


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

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


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


Integrate the following functions w.r.t. x : `cosx/sin(x - a)`


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


Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`


Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`


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

cos8xcotx


Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`


Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`


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


Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`


Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`


Evaluate the following integrals:

`int (7x + 3)/sqrt(3 + 2x - x^2).dx`


Choose the correct options from the given alternatives :

`int sqrt(cotx)/(sinx*cosx)*dx` =


Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx


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


Evaluate the following.

`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx


Evaluate the following.

`int 1/(x(x^6 + 1))` dx 


Evaluate the following.

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


Evaluate the following.

`int x/(4x^4 - 20x^2 - 3)dx`


Fill in the Blank.

To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________


State whether the following statement is True or False.

If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`


Evaluate `int "x - 1"/sqrt("x + 4")` dx


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


Evaluate: `int log ("x"^2 + "x")` dx


`int cos sqrtx` dx = _____________


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


`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`


`int (7x + 9)^13  "d"x` ______ + c


Evaluate `int(3x^2 - 5)^2  "d"x`


`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?


`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.


`int[ tan (log x) + sec^2 (log x)] dx= ` ______


`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.


`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.


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 dx/(2 + cos x)` = ______.

(where C is a constant of integration)


Write `int cotx  dx`.


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


`int x^3 e^(x^2) dx`


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


Evaluate:

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


If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)


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


Evaluate the following.

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


Evaluate `int1/(x(x-1))dx` 


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


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


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


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


Evaluate the following.

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×