Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
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_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
tan2(2x – 3)
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Solve: dy/dx = cos(x + y)
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Write a value of
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following integrals : `int cos^2x.dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x:
`(10x^9 10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following : `int (logx)2.dx`
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int "e"^sqrt"x"` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int cot^2x "d"x`
`int cos^7 x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int sin^-1 x`dx = ?
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int (cos x)/(1 - sin x) "dx" =` ______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int sec^6 x tan x "d"x` = ______.
`int ("d"x)/(x(x^4 + 1))` = ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate:
`int sin^3x cos^3x dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int 1/(x(x-1)) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
