Advertisements
Advertisements
प्रश्न
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
Advertisements
उत्तर
Let I = `int ("e"^(3x))/("e"^(3x) + 1) "d"x`
Put e3x + 1 = t
Differentiating w.r.t. x, we get
3e3xdx = dt
∴ e3xdx = `"dt"/3`
∴ I = `int 1/"t"* "dt"/3 = 1/3 log |"t"| + "c"`
∴ I `1/3 log|"e"^(3x) + 1| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^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)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
`int(5x + 2)/(3x - 4) dx` = ______
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^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 (5x^2 - 6x + 3)/(2x - 3) dx`
Which standard substitution is used for \[\sqrt{\mathrm{a}^2-x^2}\], \[\frac{1}{\sqrt{\mathrm{a}^2-x^2}}\], or \[\mathrm{a}^2-x^2\]?
Which standard substitution is used for \[\sqrt{x^2-a^2}\], \[\frac{1}{\sqrt{x^2-a^2}}\], or \[x^2-a^2\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
What is \[\int\cot t\,dt\] in the evaluation of \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
