Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Advertisements
उत्तर
Let I = `int (1)/(x.logx.log(logx)).dx`
= `int(1)/log(logx).(1)/(x.logx).dx`
Put log(log x) = t
∴ `(1)/logx.(1)/x.dx` = dt
∴ `(1)/(x.logx).dx` = dt
∴ I = `int (1)/t dt = log|t| + c`
= log|log (logx)| + c.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`sin x/(1+ cos x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
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 : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).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)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int cos^7 x "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int(log(logx) + 1/(logx)^2)dx` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
`int "cosec"^4x dx` = ______.
`int x^2/sqrt(1 - x^6)dx` = ______.
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int 1/(x(x-1))dx`
