English

∫1x2-a2dx = ______.

Advertisements
Advertisements

Question

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

Fill in the Blanks
Advertisements

Solution

`int 1/sqrt(x^2 - a^2)dx` = `bb(underline(log|x + sqrt(x^2 - a^2)| + c)`.

shaalaa.com
  Is there an error in this question or solution?
2025-2026 (March) Model set 2 by shaalaa.com

RELATED QUESTIONS

Integrate : sec3 x w. r. t. x.


`int e^x sec x (1 +   tan x) dx` equals:


Find : 

`∫(log x)^2 dx`


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


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


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

`e^(5x).[(5x.logx + 1)/x]`


Integrate the following with respect to the respective variable : cos 3x cos 2x cos x


Integrate the following w.r.t.x : log (log x)+(log x)–2 


Evaluate the following.

`int x^2 e^4x`dx


Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx


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


Evaluate: `int "dx"/(5 - 16"x"^2)`


`int (cos2x)/(sin^2x cos^2x)  "d"x`


`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`


Evaluate `int 1/(x(x - 1))  "d"x`


`int logx/(1 + logx)^2  "d"x`


Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`


Find: `int e^x.sin2xdx`


Solution of the equation `xdy/dx=y log y` is ______


Solve the differential equation (x2 + y2) dx - 2xy dy = 0 by completing the following activity.

Solution: (x2 + y2) dx - 2xy dy = 0

∴ `dy/dx=(x^2+y^2)/(2xy)`                      ...(1)

Puty = vx

∴ `dy/dx=square`

∴ equation (1) becomes

`x(dv)/dx = square`

∴ `square  dv = dx/x`

On integrating, we get

`int(2v)/(1-v^2) dv =intdx/x`

∴ `-log|1-v^2|=log|x|+c_1`

∴ `log|x| + log|1-v^2|=logc       ...["where" - c_1 = log c]`

∴ x(1 - v2) = c

By putting the value of v, the general solution of the D.E. is `square`= cx


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


Evaluate the following.

`intx^3  e^(x^2) dx`


Complete the following activity:

`int_0^2 dx/(4 + x - x^2) `

= `int_0^2 dx/(-x^2 + square + square)`

= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`

= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`

= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`


Evaluate the following:

`intx^3e^(x^2)dx` 


Evaluate:

`int x^2 cos x  dx`


Evaluate the following.

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


Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]


Which substitution can also be used before integrating by parts for \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx?\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×