Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Advertisements
उत्तर
`int sinx/(1 + sinx)dx`
= `int sinx/(1 + sinx) xx (1 - sinx)/(1 - sinx)dx`
= `int(sinx - sin^2x)/(1 - sin^2x)dx`
= `int (sinx - sin^2x)/cos^2x dx`
= `int(sinx/cos^2x - sin^2x/cos^2x)dx`
= `int(1/cosx)(sinx/cosx)dx - int tan^2x dx`
= `int sec x tan x dx - int (sec^2x - 1)dx`
= `int sec x tan x dx - int sec^2x dx + int 1 dx`
= sec x – tan x + x + c.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
`int (sin4x)/(cos 2x) "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int x^3"e"^(x^2) "d"x`
`int sec^6 x tan x "d"x` = ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int 1/(x(x-1)) dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
