Advertisements
Advertisements
प्रश्न
`int "dx"/(9"x"^2 + 1)= ______. `
विकल्प
`1/3 "tan"^-1(2"x") +"c"`
`1/3 "tan"^-1"x" +"c"`
`1/3 "tan"^-1(3"x") +"c"`
`1/3 "tan"^-1(6"x") +"c"`
Advertisements
उत्तर
`1/3 "tan"^-1(3"x") +"c"`
Let I = `int "dx"/(9"x"^2 + 1)`
= `1/9 int "dx"/(("x"^2) +(1/3)^2)`
= `1/9 1/(1/3) "tan"^-1("x"/(1/3)) + "C"`
`= 1/3 "tan"^-1(3"x") + "c"`
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int (cos2x)/(sin^2x) "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
`int dx/(1 + e^-x)` = ______
`int (cos x)/(1 - sin x) "dx" =` ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int sqrt(x^2 - a^2)/x dx` = ______.
Evaluate the following
`int1/(x^2 +4x-5)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(5x^2-6x+3)/(2x-3) dx`
