Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Advertisements
उत्तर
Let I = `int (e^(2x) + 1)/(e^(2x) - 1).dx`
= `int (((e^(2x) + 1)/(e^x)))/(((e^(2x) - 1)/(e^x))).dx`
= `int((e^x + e^(-x))/(e^x - e^-x)).dx`
= `int (d/dx(e^x - e^-x))/(e^x - e^-x).dx`
= log|ex – e–x| + c. ...`[∵ int (f'(x))/f(x).dx= log|f(x)| + c]`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find `intsqrtx/sqrt(a^3-x^3)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:
`(sin x)/(1+ cos x)^2`
Write a value of
Write a value of
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int dx/(1 + e^-x)` = ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
Evaluate `int(1 + x + x^2/(2!))dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
