English

∫xx+2 dx - Mathematics and Statistics

Advertisements
Advertisements

Question

`int x/(x + 2)  "d"x`

Sum

Solution

`int x/(x + 2)  "d"x = int ((x + 2) - 2)/(x + 2) "d"x`

= `int(1 - 2/(x + 2)) "d"x`

= `int 1 *"d"x - 2 int 1/(x + 2)  "d"x`

= x − 2log |x + 2| + c

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

APPEARS IN

RELATED QUESTIONS

Integrate the functions:

(4x + 2) `sqrt(x^2 + x +1)`


Integrate the functions:

`x^2/(2+ 3x^3)^3`


Integrate the functions:

`1/(x(log x)^m),  x > 0, m ne 1`


Integrate the functions:

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


Integrate the functions:

sec2(7 – 4x)


Integrate the functions:

`1/(1 - tan x)`


Integrate the functions:

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


Evaluate `int 1/(3+ 2 sinx + cosx) dx`


Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`


\[\int\sqrt{9 - x^2}\text{ dx}\]

Write a value of

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

Write a value of

\[\int x^2 \sin x^3 \text{ dx }\]

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


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\[\int \log_e x\ dx\].

 


Write a value of\[\int a^x e^x \text{ dx }\]


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


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

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


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


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

Evaluate the following integrals : tan2x dx


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


Evaluate the following integrals:

`int (cos2x)/sin^2x dx` 


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


Evaluate the following integrals:

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


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


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 : `3^(cos^2x) sin 2x`


Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`


Choose the correct options from the given alternatives :

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


Choose the correct options from the given alternatives :

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


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


Evaluate the following.

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


Evaluate the following.

`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx


Evaluate the following.

∫ (x + 1)(x + 2)7 (x + 3)dx


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 (5x^2 - 6x + 3)/(2x − 3)` dx


`int 1/(cos x - sin 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 (sin4x)/(cos 2x) "d"x`


`int 1/(xsin^2(logx))  "d"x`


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


State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`


`int (1 + x)/(x + "e"^(-x))  "d"x`


`int1/(4 + 3cos^2x)dx` = ______ 


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


`int(7x - 2)^2dx = (7x -2)^3/21 + c`


`int (sin  (5x)/2)/(sin  x/2)dx` is equal to ______. (where C is a constant of integration).


If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.


`int (x + sinx)/(1 + cosx)dx` is equal to ______.


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


`int dx/(2 + cos x)` = ______.

(where C is a constant of integration)


Write `int cotx  dx`.


Evaluate the following.

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


Evaluate the following.

`int 1/(x^2 + 4x - 5)  dx`


Evaluate the following.

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


Evaluate the following.

`int x sqrt(1 + x^2)  dx`


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


Evaluate:

`int sqrt((a - x)/x) dx`


Evaluate:

`int(sqrt(tanx) + sqrt(cotx))dx`


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


Evaluate:

`int(cos 2x)/sinx dx`


Evaluate:

`int sin^3x cos^3x  dx`


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


Evaluate:

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


Evaluate.

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


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×