Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Advertisements
उत्तर
Let `I = int (e^(2x) - 1)/(e^(2x) + 1)` dx
On dividing the numerator and denominator by ex
`= int (e^x - e^(-x))/(e^x + e^(-x))` dx
Put ex + e-x = t
Then, ex - e-x dx = dt
Hence, `I = int 1/t` dt
= log t + C
= log (ex + e-x) + C
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Integrate the functions:
`sin x/(1+ cos x)`
Solve:
dy/dx = cos(x + y)
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of
Write a value of\[\int \log_e x\ dx\].
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
`int (sin4x)/(cos 2x) "d"x`
`int logx/x "d"x`
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 ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Find `int dx/sqrt(sin^3x cos(x - α))`.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
