English

∫2(cos2x-sin2x)cos2x+sin2x dx = ______________

Advertisements
Advertisements

Question

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

Options

  • sin 2x + c

  • cos 2x + c

  • tan 2x + c

  • 2 sin 2x + c

MCQ
Fill in the Blanks
Advertisements

Solution

sin 2x + c

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

RELATED QUESTIONS

Find `intsqrtx/sqrt(a^3-x^3)dx`


Integrate the functions:

`xsqrt(1+ 2x^2)`


Integrate the functions:

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


Integrate the functions:

sec2(7 – 4x)


Integrate the functions:

`sqrt(sin 2x) cos 2x`


Write a value of

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

Write a value of

\[\int e^x \sec x \left( 1 + \tan x \right) \text{ dx }\]

Write a value of

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

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

 


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


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


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

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


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


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

 Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log  |"x" +sqrt("x"^2 +"a"^2) | + "c"`


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


Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`


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


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


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


Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`


Choose the correct option from the given alternatives : 

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


Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`


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


Evaluate the following.

`int (1 + "x")/("x" + "e"^"-x")` dx


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


State whether the following statement is True or False.

The proper substitution for `int x(x^x)^x (2log x + 1)  "d"x` is `(x^x)^x` = t


Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx


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


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


`int (sin4x)/(cos 2x) "d"x`


`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`


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

`int3^(2x + 3)  "d"x = (3^(2x + 3))/2 + "c"`


`int (cos x)/(1 - sin x) "dx" =` ______.


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


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


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


`int dx/((x+2)(x^2 + 1))`    ...(given)

`1/(x^2 +1) dx = tan ^-1 + c`


Evaluate 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 the following.

`int1/(x^2 + 4x - 5)  dx`


Evaluate the following.

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×