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
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Evaluate: `int 1/(x(x-1)) dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log 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 : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
`int sqrt(1 + "x"^2) "dx"` =
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate `int 1/((2"x" + 3))` dx
`int (log x)/(log ex)^2` dx = _________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int x/(x + 2) "d"x`
`int cos^7 x "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int1/(x(x-1))dx`
