Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Advertisements
उत्तर
Let I = `int sqrt(tanx)/(sin x . cosx).dx`
Dividing numerator and denominator by cos2x, we get
I = `int(((sqrttanx)/(cos^2x)))/((sinx/cosx)).dx`
= `int (sqrt(tanx).sec^2x)/tanx.dx`
= `int sec^2x/sqrt(tanx).dx`
Put tan x = t
∴ sec2xdx = dt
∴ I = `int (1)/sqrt(t)dt`
= `int t^(-1/2) dt`
= `t^(1/2)/(1/2) + c`
= `2sqrt(t) + c`
= `2sqrt(tanx) + c`.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int sinx/(sin 3x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).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 x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int(1 - x)^(-2) dx` = ______.
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int sqrt(x^2 - a^2)/x dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int(1+x+x^2/(2!))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
