Advertisements
Advertisements
प्रश्न
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
Advertisements
उत्तर
Let I = `int "e"^"x"/(4"e"^"2x" -1)` dx
`"I" = int "e"^"x"/(4("e"^"x")^2 - 1)` dx
Put ex = t
∴ ex dx = dt
∴ I = `int "dt"/(4"t"^2 - 1)`
`∴ "I" = 1/4 int 1/("t"^2 - 1/4)` dt
`∴ "I" = 1/4 int 1/("t"^2 - (1/2)^2)` dt
`∴ "I" = 1/4 . 1/(2 (1/2)) log |("t" - 1/2)/("t" + 1/2)|` + c
`∴ "I" = 1/4 log |("2t" - 1)/("2t" + 1)|` + c
Resubstitute t = ex
`∴ "I" = 1/4 log |(2"e"^"x" - 1)/(2"e"^"x" + 1)|` + c
Notes
Answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
Integrate the function in (sin-1x)2.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
`int 1/x "d"x` = ______ + c
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
Evaluate `int 1/(4x^2 - 1) "d"x`
`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
Solve: `int sqrt(4x^2 + 5)dx`
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Evaluate the following.
`int x^3 e^(x^2) dx`
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
Evaluate:
`int (logx)^2 dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
