Advertisements
Advertisements
प्रश्न
Evaluate : \[\int\frac{1}{x(1 + \log x)} \text{ dx}\]
Advertisements
उत्तर
I = \[\int\frac{1}{x\left( 1 + \log x \right)} \text{ dx }\]
Let (1 + log x) = t
or,\[ \frac{1}{x}dx = dt\]
\[ \Rightarrow I = \int\frac{1}{t}dt\]
\[\Rightarrow I = \text{ log }\left| t \right| + C\]
\[ \therefore I = \text{ log}\left| 1 + \log x \right| + C\]
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^3dx/(9+x^2)`
Evaluate the following integrals:
\[\int\frac{1}{\sqrt{1 - x^2} \left( \sin^{- 1} x \right)^2} dx\]
Evaluate the following integrals:
Evaluate the following integrals:
Evaluate the following integrals:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Write a value of
Evaluate:\[\int\frac{x^2}{1 + x^3} \text{ dx }\] .
Evaluate:\[\int\frac{\cos \sqrt{x}}{\sqrt{x}} \text{ dx }\]
Evaluate:\[\int \sec^2 \left( 7 - 4x \right) \text{ dx }\]
Evaluate: \[\int 2^x \text{ dx }\]
Evaluate: \[\int\frac{x^3 - x^2 + x - 1}{x - 1} \text{ dx }\]
Write the value of\[\int\sec x \left( \sec x + \tan x \right)\text{ dx }\]
Evaluate: \[\int\frac{1}{x^2 + 16}\text{ dx }\]
Evaluate: \[\int\left( 1 - x \right)\sqrt{x}\text{ dx }\]
Evaluate:
`∫ (1)/(sin^2 x cos^2 x) dx`
Evaluate: `int_ (x + sin x)/(1 + cos x ) dx`
Evaluate the following:
`int sqrt(1 + x^2)/x^4 "d"x`
Evaluate the following:
`int sqrt(2"a"x - x^2) "d"x`
