मराठी

Integrate the functions: 2x1+x2

Advertisements
Advertisements

प्रश्न

Integrate the functions:

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

बेरीज
Advertisements

उत्तर

Let I `= int (2x)/(1 + x^2)`

Taking = 1 + x2 

2x dx = dt

∴ `I  = int (2x)/(1 + x^2)  dx int 1/t dt`

I = log t + C = log (1 + x2) + C

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Integrals - Exercise 7.2 [पृष्ठ ३०४]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 7 Integrals
Exercise 7.2 | Q 1 | पृष्ठ ३०४

संबंधित प्रश्‍न

Integrate the functions:

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


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


Write a value of

\[\int e^x \left( \sin x + \cos x \right) \text{ dx}\]

 


Write a value of

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

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


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

 


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


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

 

 


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


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


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


Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`


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


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


Evaluate the following integrals:

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


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


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


Evaluate the following.

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


Evaluate the following.

`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx


Evaluate the following.

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


`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


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


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


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


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


`int logx/x  "d"x`


`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`


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


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


`int1/(4 + 3cos^2x)dx` = ______ 


`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`


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


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


Evaluate the following.

`int 1/(x^2+4x-5)  dx`


Evaluate.

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


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


`int 1/(sin^2x cos^2x)dx` = ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×