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

∫cot2x dx - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

`int cot^2x  "d"x`

बेरीज

उत्तर

`int cot^2x  "d"x = int("cosec"^2x - 1)  "d"x`

= −cot x − x + c

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

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Evaluate :   `∫1/(cos^4x+sin^4x)dx`


Integrate the functions:

`(log x)^2/x`


Integrate the functions:

`1/(x-sqrtx)`


Integrate the functions:

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


Integrate the functions:

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


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


Evaluate: `int (sec x)/(1 + cosec x) dx`


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

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

\[\int\cos x \sqrt{4 - \sin^2 x}\text{ dx}\]

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

Write a value of

\[\int \tan^3 x \sec^2 x \text{ dx }\].

 


 Write a valoue of \[\int \sin^3 x \cos x\ dx\]

 


Write a value of

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

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


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

 


Evaluate:  \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]


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


Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`


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


Evaluate the following integrals : `int sinx/(1 + sinx)dx`


Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`


Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`


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


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


Evaluate the following integrals:

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


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


Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`


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


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

`(10x^9  10^x.log10)/(10^x + x^10)`


Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.


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


Integrate the following functions w.r.t. x : cos7x


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


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


Evaluate the following : `int (1)/(7 + 2x^2).dx`


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


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


Evaluate the following:

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


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


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


Evaluate the following integrals:

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


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


Choose the correct options from the given alternatives : 

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


Choose the correct options from the given alternatives :

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


Integrate the following with respect to the respective variable:

`x^7/(x + 1)`


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


If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).


Evaluate the following.

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


Evaluate the following.

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


Choose the correct alternative from the following.

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


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


Evaluate `int (5"x" + 1)^(4/9)` dx


Evaluate: `int log ("x"^2 + "x")` dx


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


If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______


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


State whether the following statement is True or False:

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


State whether the following statement is True or False:

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


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


`int sec^6 x tan x   "d"x` = ______.


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


Write `int cotx  dx`.


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


Evaluate the following.

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


if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`


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 the following.

`intx sqrt(1 +x^2)  dx`


Evaluate the following.

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


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


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


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


Evaluate the following.

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×