English

∫ ex(x-1)x2 dx = ______ - Mathematics and Statistics

Advertisements
Advertisements

Question

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

Options

  • `x"e"^(-x) + c`

  • `("e"^x)/(x^2) + c`

  • `(x - 1/x)"e"^x + c`

  • `("e"^x)/x + c`

MCQ
Fill in the Blanks
Advertisements

Solution

`("e"^x)/x + c`

shaalaa.com
  Is there an error in this question or solution?
Chapter 2.3: Indefinite Integration - MCQ

RELATED QUESTIONS

Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`


Integrate the functions:

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


Integrate the functions:

`1/(x + x log x)`


Integrate the functions:

sin (ax + b) cos (ax + b)


Integrate the functions:

cot x log sin x


Integrate the functions:

`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`


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


Write a value of

\[\int\frac{1 + \cot x}{x + \log \sin x} \text{ dx }\]

Write a value of\[\int \cos^4 x \text{ sin x dx }\]


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

 


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


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

 

 


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


Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1 


Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`


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


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

`(sinx cos^3x)/(1 + cos^2x)`


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


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


If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).


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


Evaluate the following.

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


Evaluate the following.

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


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


Evaluate: ∫ |x| dx if x < 0


Evaluate: `int log ("x"^2 + "x")` dx


Evaluate: `int "e"^sqrt"x"` dx


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


`int cos sqrtx` dx = _____________


`int sqrt(1 + sin2x)  dx`


`int cos^7 x  "d"x`


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)`


State whether the following statement is True or False:

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


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


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


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 ______.


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


Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.


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


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


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


Evaluate:

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


Evaluate.

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


Evaluate `int1/(x(x-1))dx` 


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


Evaluate the following.

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


Evaluate the following.

`int1/(x^2 + 4x-5)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×