Evaluate: `Int (2y^2)/(Y^2 + 4)Dx` - Mathematics

Advertisements
Advertisements

Evaluate: `int (2y^2)/(y^2 + 4)dx`

Advertisements

Solution

`I = int (2y^2)/(y^2 + 4) dy`

`= int(2y^2 + 8 - 8)/(y^2 + 4) dy`

`= 2int (y^2 + 4)/(y^2 + 4) dy - 8 int dy/(y^2 + 2^2)`

`= 2y - 4tan^(-1) (y/2) + c`

  Is there an error in this question or solution?
2014-2015 (March)

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`


Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Find : `int(x+3)sqrt(3-4x-x^2dx)`


Find `intsqrtx/sqrt(a^3-x^3)dx`


Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.


Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`


Evaluate: `int sqrt(tanx)/(sinxcosx) dx`


Integrate the functions:

`xsqrt(x + 2)`


Integrate the functions:

`x/(sqrt(x+ 4))`, x > 0 


Integrate the functions:

`(2cosx - 3sinx)/(6cos x + 4 sin x)`


Integrate the functions:

`sqrt(sin 2x) cos 2x`


Integrate the functions:

`cos x /(sqrt(1+sinx))`


Integrate the functions in `(x^3 sin(tan^(-1) x^4))/(1 + x^8)`


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


Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`


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


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

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

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

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

\[\int\sqrt{16 x^2 + 25} \text{ dx}\]

\[\int\sqrt{4 x^2 - 5}\text{ dx}\]

\[\int\sqrt{2 x^2 + 3x + 4} \text{ dx}\]

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

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

 


Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .

Write a value of\[\int \cos^4 x \text{ sin x dx }\]


Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]


Write a value of\[\int\left( e^{x \log_e \text{  a}} + e^{a \log_e x} \right) dx\] .


Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]


Write a value of

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

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

 


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

The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is


\[\int x \sin^3 x\ dx\]

`int "dx"/(9"x"^2 + 1)= ______. `


Integrate the following w.r.t. x : `2x^3 - 5x + 3/x + 4/x^5`


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


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


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


Evaluate the following integrals:

`int x/(x + 2).dx`


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


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


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


Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`


If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)


Integrate the following functions w.r.t. x : `(logx)^n/x`


Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`


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


Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`


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 : `x^2/sqrt(9 - x^6)`


Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`


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


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


Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`


Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`


Integrate the following functions w.r.t. x : tan5x


Integrate the following functions w.r.t. x :  tan 3x tan 2x tan x


Integrate the following functions w.r.t. x : sin5x.cos8x


Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`


Evaluate the following : `int (1)/(25 - 9x^2).dx`


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


Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`


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


Evaluate the following : `int  (1)/(x^2 + 8x + 12).dx`


Evaluate the following : `(1)/(4x^2 - 20x + 17)`


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


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


Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`


Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`


Evaluate the following integrals:

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


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


Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`


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


Choose the correct option from the given alternatives : 

`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =


`int logx/(log ex)^2*dx` = ______.


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =


integrate the following with respect to the respective variable : `x^2/(x + 1)`


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


Evaluate the following.

`int 1/("x" log "x")`dx


Evaluate the following.

`int 1/("x"("x"^6 + 1))` dx


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx


Evaluate the following.

`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx


Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx


Choose the correct alternative from the following.

`int "x"^2 (3)^("x"^3) "dx"` =


Fill in the Blank.

To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________


Evaluate: ∫ |x| dx if x < 0


Evaluate: `int "x" * "e"^"2x"` dx


Evaluate: `int log ("x"^2 + "x")` dx


`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________


`int cos sqrtx` 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 sqrt(1 + sin2x)  "d"x`


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


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


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


`int x/(x + 2)  "d"x`


`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1))  "d"x`


Choose the correct alternative:

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


State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`


State whether the following statement is True or False:

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


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 x^3"e"^(x^2) "d"x`


`int (1 + x)/(x + "e"^(-x))  "d"x`


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


`int1/(4 + 3cos^2x)dx` = ______ 


General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)


`int[ tan (log x) + sec^2 (log x)] dx= ` ______


`int sec^6 x tan x   "d"x` = ______.


`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.


`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.


If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.


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


`int(log(logx) + 1/(logx)^2)dx` = ______.


`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.


The value of `intsinx/(sinx - cosx)dx` equals ______.


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 ______.


The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.


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


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


`int x/sqrt(1 - 2x^4) dx` = ______.

(where c is a constant of integration)


Write `int cotx  dx`.


`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`


Evaluate.

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


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


Prove that:

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


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


Evaluate:

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


Evaluate:

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


Evaluate:

`int sin^2(x/2)dx`


Evaluate.

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


Evaluate the following.

`intx sqrt(1 +x^2)  dx`


Evaluate:

`int(cos 2x)/sinx dx`


Evaluate:

`int sin^3x cos^3x  dx`


Evaluate the following.

`intxsqrt(1+x^2)dx`


The value of `int dx/(sqrt(1 - x))` is ______.


Evaluate the following.

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


Evaluate `int1/(x(x-1))dx` 


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


Evaluate the following.

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


Share
Notifications



      Forgot password?
Use app×