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

Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`


 
 

Evaluate :

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

 
 

Integrate the functions:

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


Integrate the functions:

`xsqrt(x + 2)`


Integrate the functions:

`cos sqrt(x)/sqrtx`


Integrate the functions:

`sin x/(1+ cos x)`


Integrate the functions:

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


Solve:

dy/dx = cos(x + y)


\[\int\sqrt{x^2 + x + 1} \text{ dx}\]

Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].


Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]


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


Write a value of

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

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


Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].


Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]


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


Evaluate the following integrals : `int tanx/(sec x + tan x)dx`


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


Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`


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


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

`x^5sqrt(a^2 + x^2)`


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


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =


Choose the correct options from the given alternatives :

`int (e^(2x) + e^-2x)/e^x*dx` =


Evaluate the following.

`int 1/("x" log "x")`dx


Evaluate the following.

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


Evaluate the following.

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


Evaluate `int 1/((2"x" + 3))` dx


Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx


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


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


`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.


`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 ______.


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


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


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


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


`int x^2/sqrt(1 - x^6)dx` = ______.


Evaluate the following.

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


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


Evaluate the following:

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


Evaluate the following

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


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


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


For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?


Which expression results after simplifying \[\int\frac{\sin(t-a)}{\sin t}\,dt\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×