Advertisements
Advertisements
Question
Integrate the functions:
`1/(x + x log x)`
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate :`intxlogxdx`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Write a value of
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
`int sqrt(1 + "x"^2) "dx"` =
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int cos^7 x "d"x`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int (f^'(x))/(f(x))dx` = ______ + c.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`intsqrt(sec x/2 - 1)dx`
