Advertisements
Advertisements
प्रश्न
Integrate the functions:
`1/(x + x log x)`
उत्तर
Let I `= int 1/(x + x log x)` dx
or I `= int 1/(x (1+ log x)` dx
Put 1 + log x = t
`1/x` dx = dt
Hence, I `= int 1/t` dt
= log t + C
= log (1 + log x) + C
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following : `int (logx)2.dx`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
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 log ("x"^2 + "x")` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int(log(logx))/x "d"x`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
Write `int cotx dx`.
`int x^3 e^(x^2) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`