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:
sin3 (2x + 1)
Find the integrals of the function:
sin3 x cos3 x
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:
tan3 2x sec 2x
Find the integrals of the function:
tan4x
Find the integrals of the function:
sin−1 (cos x)
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
Find `int_ (log "x")^2 d"x"`
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: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Find: `int sin^-1 (2x) dx.`
Evaluate `int tan^8 x sec^4 x"d"x`
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int sqrt(1 + sinx)"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`
`int sinx/(3 + 4cos^2x) "d"x` = ______.
The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4 dx` is
What does integration using trigonometric identities mean?
Using \(\cos^2 x = \frac{1+\cos 2x}{2}\), which expression is equivalent to \(\int \cos^2 x\,dx\)?
What should be done first when evaluating an integral containing a complicated trigonometric expression?
After a trigonometric expression has been simplified, how should it be integrated?
What must always be added to an indefinite integral?
