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 (sinx)/sqrt(36-cos^2x)dx`
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int \log_e x\ dx\].
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int (log x)/(log ex)^2` dx = _________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int dx/(1 + e^-x)` = ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
