Advertisements
Advertisements
प्रश्न
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
विकल्प
tan x + cot x + C
tan x + cosec x + C
− tan x + cot x + C
tan x + sec x + C
Advertisements
उत्तर
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to tan x + cot x + C.
Explanation:
Let I = `int (sin^2 x - cos^2 x)/(sin^2 x cos^2 x) dx`
`= int ((sin^2 x)/(sin^2 x cos^2 x) - (cos^2 x)/(sin^2 x cos^2 x))`
`= int (1/(cos^2 x) - 1/(sin^2 x)) dx`
`= int (sec^2 x - cosec^2 x) dx`
`= tan x + cot x + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
cos 2x cos 4x cos 6x
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:
`(1-cosx)/(1 + cos x)`
Find the integrals of the function:
cos4 2x
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^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
`(cos 2x+ 2sin^2x)/(cos^2 x)`
Find the integrals of the function:
`1/(sin xcos^3 x)`
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (log "x")^2 d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `int sin^-1 (2x) dx.`
Find `int "dx"/(2sin^2x + 5cos^2x)`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
`int (sin^6x)/(cos^8x) "d"x` = ______.
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 sqrt(1 + sinx)"d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
`int (cos^2x)/(sin x + cos x)^2 dx` is equal to
