Advertisements
Advertisements
Question
Find: `int logx/(1 + log x)^2 dx`
Advertisements
Solution
`int logx/(1 + log x)^2 dx = int (log x + 1 - 1)/(1 + log x)^2 dx`
= `int 1/(1 + log x) dx - int 1/(1 + log x)^2 dx`
= `1/(1 + log x) xx x - int (-1)/(1 + log x)^2 xx 1/x xx xdx - int 1/(1 + log x)^2 dx`
= ` x/(1 + log x) + c`
APPEARS IN
RELATED QUESTIONS
Evaluate the following integral:
If f(2a − x) = −f(x), prove that
Solve each of the following integral:
Evaluate :
Evaluate : \[\int\limits_0^{2\pi} \cos^5 x dx\] .
\[\int\limits_0^1 \tan^{- 1} x dx\]
\[\int\limits_0^{\pi/2} x^2 \cos 2x dx\]
\[\int\limits_0^1 \left| 2x - 1 \right| dx\]
\[\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}} dx\]
\[\int\limits_0^1 \cot^{- 1} \left( 1 - x + x^2 \right) dx\]
Using second fundamental theorem, evaluate the following:
`int_0^(1/4) sqrt(1 - 4) "d"x`
Choose the correct alternative:
If f(x) is a continuous function and a < c < b, then `int_"a"^"c" f(x) "d"x + int_"c"^"b" f(x) "d"x` is
Find `int sqrt(10 - 4x + 4x^2) "d"x`
Evaluate `int (x^2 + x)/(x^4 - 9) "d"x`
If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4ex + 5e –x| + C, then ______.
