Advertisements
Advertisements
प्रश्न
Find the integrals of the function:
`1/(sin xcos^3 x)`
Advertisements
उत्तर
Let `I = int 1/(sin x cos^3 x) dx`
`= int (sin^2 x + cos^2 x)/(sin x cos^3 x) dx`
`= int ((sin^2 x)/(sin x cos^3 x) + (cos^2 x)/(sin x cos^3 x)) dx`
`= int ((sin x)/(cos 3 x) + (cos x)/(sin x cos^2 x)) dx`
`= int (tan x sec^2 x + (sec^2 x)/(tan x)) dx`
`= int (tan x + 1/(tan x)) sec^2 x dx`
Put tan x = t
⇒ sec2 x dx = dt
∴ `I = int (t + 1/t) dt `
`= t^2/2 + log |t| + C`
`log |tan x| + 1/2 tan^2 x + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin 3x cos 4x
Find the integrals of the function:
cos 2x cos 4x cos 6x
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
sin3 x cos3 x
Find the integrals of the function:
sin x sin 2x sin 3x
Find the integrals of the function:
sin 4x sin 8x
Find the integrals of the function:
`cos x/(1 + cos x)`
Find the integrals of the function:
`(sin^2 x)/(1 + cos x)`
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Find the integrals of the function:
tan4x
Find the integrals of the function:
`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
Evaluate `int_0^(3/2) |x sin pix|dx`
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ (log "x")^2 d"x"`
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Find: `int sin^-1 (2x) dx.`
Find `int x^2tan^-1x"d"x`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
Evaluate the following:
`int (cosx - cos2x)/(1 - cosx) "d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
`int sinx/(3 + 4cos^2x) "d"x` = ______.
