English

∫1x2-a2 dx = ______ + c

Advertisements
Advertisements

Question

`int 1/(x^2 - "a"^2)  "d"x` = ______ + c

Fill in the Blanks
Advertisements

Solution

`1/(2"a") log |(x - "a")/(x + "a")|` 

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.5: Integration - Q.2

RELATED QUESTIONS

Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.


Evaluate the following: `int x.sin^-1 x.dx`


Evaluate the following : `int sin θ.log (cos θ).dθ`


Evaluate the following : `int cos(root(3)(x)).dx`


Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`


Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex  


Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`


Choose the correct options from the given alternatives :

`int (1)/(cosx - cos^2x)*dx` =


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


Integrate the following w.r.t.x : cot–1 (1 – x + x2)


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


Evaluate the following.

∫ x log x dx


Choose the correct alternative from the following.

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx"` = 


Evaluate: `int "dx"/("9x"^2 - 25)`


Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`


`int logx/(1 + logx)^2  "d"x`


`int log x * [log ("e"x)]^-2` dx = ?


`int tan^-1 sqrt(x)  "d"x` is equal to ______.


The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1)  dx` is


If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.


If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.


`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.


`int(xe^x)/((1+x)^2)  dx` = ______


The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.


Evaluate the following.

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


Integration by parts is a method of integration based on which rule of differentiation?


Which pair is listed as Exponential in the LIATE rule?


Let \[I=\int e^x\sin x\,dx.\] After applying integration by parts once, which equation is obtained?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×