Advertisements
Advertisements
प्रश्न
`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.
पर्याय
log |1 + cosx| + C
log |x + sinx| + C
`x - tan x/2 + "C"`
`x.tan x/2 + "C"`
उत्तर
`int (x + sinx)/(1 + cosx) "d"x` is equal to `x.tan x/2 + "C"`.
Explanation:
I = `int (x + sinx)/(1 + cosx) "d"x`
= `int x/(1 + cos x) "d"x + int (sinx)/(1 + cosx) "d"x`
= `int x/(2cos^2 x/2) "d"x + int (2sin x/2 cos x/2)/(2cos^2 x/2) "d"x`
= `int x sec^2 x/2 "d"x + int tan x/2 "d"x`
= `1/2 [x*2 tan x/2 - int 2 tan x/2 "d"x] + int tan x/2 "d"x`
= `x * tan x/2 + "C"`
APPEARS IN
संबंधित प्रश्न
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 4x sin 8x
Find the integrals of the function:
`cos x/(1 + cos x)`
Find the integrals of the function:
sin4 x
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))`
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Evaluate `int_0^pi (x sin x)/(1 + cos^2 x) dx`
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Find `int_ (log "x")^2 d"x"`
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int "dx"/(2sin^2x + 5cos^2x)`
Find `int x^2tan^-1x"d"x`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
Evaluate the following:
`int ("d"x)/(1 + cos x)`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
Evaluate the following:
`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4 dx` is
`int (cos^2x)/(sin x + cos x)^2 dx` is equal to
