Advertisements
Advertisements
प्रश्न
The value of \[\int\frac{1}{x + x \log x} dx\] is
पर्याय
1 + log x
x + log x
x log (1 + log x)
log (1 + log x)
Advertisements
उत्तर
log (1 + log x)
\[\text{Let }I = \int\frac{dx}{x + x \log x}\]
\[ \Rightarrow \int\frac{dx}{x \left( 1 + \log x \right)}\]
\[\text{Putting }1 + \log x = t\]
\[\Rightarrow \frac{1}{x} dx = dt\]
\[ \therefore I = \int\frac{dt}{t}\]
\[ = \ln \left| t \right| + C\]
\[ = \ln \left| 1 + \log x \right| + C\]
APPEARS IN
संबंधित प्रश्न
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Evaluate: `int 1/(x(x-1)) dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
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 sqrt(x^2 - 8x + 7)` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int cos sqrtx` dx = _____________
`int 1/(xsin^2(logx)) "d"x`
`int(log(logx))/x "d"x`
`int(1 - x)^(-2) dx` = ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int "cosec"^4x dx` = ______.
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
How should a substitution be chosen?
