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(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
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 "x - 1"/sqrt("x + 4")` dx
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int logx/x "d"x`
`int(log(logx))/x "d"x`
`int cos^3x dx` = ______.
Write `int cotx dx`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
