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

∫exx[x(logx)2+2logx] dx = ______________ - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________

पर्याय

  • ex log x + c

  • ex (log x)2 + c

  • e2x log x + c

  • e2x (log x)2 + c

MCQ
रिकाम्या जागा भरा

उत्तर

ex (log x)2 + c

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2.3: Indefinite Integration - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Integrate the functions:

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


Integrate the functions:

`(log x)^2/x`


Integrate the functions:

sin x ⋅ sin (cos x)


Integrate the functions:

`(2cosx - 3sinx)/(6cos x + 4 sin x)`


Integrate the functions:

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


Integrate the functions:

cot x log sin x


Integrate the functions:

`sqrt(tanx)/(sinxcos x)`


Integrate the functions:

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


`int (dx)/(sin^2 x cos^2 x)` equals:


Solve: dy/dx = cos(x + y)


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

Write a value of

\[\int\frac{\cos x}{3 + 2 \sin x}\text{  dx}\]

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


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

 


Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].


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

 


Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .


The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is


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


\[\int\frac{\cos^5 x}{\sin x} \text{ dx }\]

Integrate the following w.r.t. x:

`2x^3 - 5x + 3/x + 4/x^5`


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 x/(x + 2).dx`


Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`


Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`


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


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

x9.sec2(x10)


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

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


Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`


Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`


Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`


Integrate the following functions w.r.t. x :  tan 3x tan 2x tan x


Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`


Evaluate the following : `int sinx/(sin 3x).dx`


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


Evaluate the following integrals:

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


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


Choose the correct options from the given alternatives :

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


Choose the correct options from the given alternatives : 

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


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


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


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt"x" + "x")` dx


Evaluate the following.

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


Evaluate the following.

`int 1/("x"^2 + 4"x" - 5)` dx


Evaluate the following.

`int 1/(7 + 6"x" - "x"^2)` dx


Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx


Choose the correct alternative from the following.

The value of `int "dx"/sqrt"1 - x"` is


`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c


If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______


Fill in the Blank.

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


Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).


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


`int 1/(cos x - sin x)` dx = _______________


`int sqrt(x^2 + 2x + 5)` dx = ______________


`int cos sqrtx` dx = _____________


`int (log x)/(log ex)^2` dx = _________


`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`


`int (cos2x)/(sin^2x)  "d"x`


Choose the correct alternative:

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


State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`


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


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


`int(5x + 2)/(3x - 4) dx` = ______


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


If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.


`int(sin2x)/(5sin^2x+3cos^2x)  dx=` ______.


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


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


`int(7x - 2)^2dx = (7x -2)^3/21 + c`


`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` = ______.


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


Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.


Evaluate the following.

`int 1/(x^2+4x-5)  dx`


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


Solve the following Evaluate.

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


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


Evaluate:

`int sin^2(x/2)dx`


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


Evaluate the following.

`intx sqrt(1 +x^2)  dx`


Evaluate:

`intsqrt(3 + 4x - 4x^2)  dx`


Evaluate:

`int sin^3x cos^3x  dx`


Evaluate the following:

`int (1) / (x^2 + 4x - 5) dx`


Evaluate the following:

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


Evaluate `int1/(x(x-1))dx` 


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×