Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(log x)^2/x`
Advertisements
उत्तर
Let `I = int (log x)^2/x` dx
Put log x = t
`1/x` dx = dt
Hence, `I = int t^2` dt
`I = t^3/3 + C`
`I = 1/3 (log x)^3 + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :`intxlogxdx`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
tan2(2x – 3)
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals:
`int (cos2x)/sin^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 : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int cos sqrtx` dx = _____________
`int (log x)/(log ex)^2` dx = _________
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
`int x^3"e"^(x^2) "d"x`
`int sec^6 x tan x "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
Evaluate `int (1+x+x^2/(2!))dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1+x+x^2/(2!))dx`
