Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(2x)/(1 + x^2)`
Advertisements
उत्तर
Let I `= int (2x)/(1 + x^2)`
Taking = 1 + x2
2x dx = dt
∴ `I = int (2x)/(1 + x^2) dx int 1/t dt`
I = log t + C = log (1 + x2) + C
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
`int (log x)/(log ex)^2` dx = _________
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int sec^6 x tan x "d"x` = ______.
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
